Essays on the Use of PLS Estimation:

For Improvement of

Non-Financial Performance Indicators

Mari Källström

Doctoral Dissertation

Department of Business Administration

Aarhus University

- 2 -

To my family

- 3 -

- 4 -

Contents

Preface ...................................................................................................................................... - 7 -

Introduction .............................................................................................................................. - 9 -

CHAPTER 1: SEM-based customer satisfaction measurement; On multicollinearity and robust

PLS estimation ........................................................................................................................ - 13 -

1.1 Introduction ................................................................................................................. - 15 -

1.2 Partial Least Squares .................................................................................................. - 17 -

1.3 Study Design ................................................................................................................ - 19 -

1.4 Results .......................................................................................................................... - 25 -

1.5 Conclusions .................................................................................................................. - 29 -

Appendix A1.1: Simulation results for Model I ............................................................... - 31 -

1.6 References .................................................................................................................... - 33 -

CHAPTER 2: Robustness in PLS estimation: Analysing the effects of introducing Non-normality

and Multicollinearity in Customer Satisfaction Measurement Data ...................................... - 37 -

2.1 Introduction ................................................................................................................. - 38 -

2.2 Estimation Procedure ................................................................................................. - 40 -

2.3 Study Design ................................................................................................................ - 43 -

2.4 Results .......................................................................................................................... - 49 -

2.6 Conclusions .................................................................................................................. - 64 -

2.7 References .................................................................................................................... - 67 -

CHAPTER 3: Enhancement of Leadership in Employee Engagement Modelling .................... - 71 -

3.1 Introduction ................................................................................................................. - 72 -

3.2 European Employee Index .......................................................................................... - 74 -

3.3 Empirical Study Design ............................................................................................... - 75 -

3.4 Results .......................................................................................................................... - 84 -

3.5 Conclusion and Discussion ....................................................................................... - 105 -

3.6 References .................................................................................................................. - 109 -

Appendix A3.1: Results on Relative effects and Relative importance for specified

analysis set-up in A) and B) ............................................................................................ - 115 -

Appendix A3.2: Results on Profile analysis - Nordic countries .................................... - 125 -

CHAPTER 4: Psychological profiling in Employee Engagement Surveys ............................... - 129 -

4.1 Introduction ............................................................................................................... - 131 -

- 5 -

4.2 Myer Briggs Type Indicator ...................................................................................... - 134 -

4.3 Data ............................................................................................................................. - 136 -

4.4 Analysis ...................................................................................................................... - 138 -

4.5 Results ........................................................................................................................ - 140 -

4.6 Discussion & Conclusion ........................................................................................... - 149 -

4.7 References .................................................................................................................. - 153 -

Appendix 4.1: Prevalence and impact structure following MBTI definition in the Nordic

countries ........................................................................................................................... - 157 -

Concluding remarks ........................................................................................................ - 161 -

- 6 -

- 7 -

Preface

The journey of this thesis began already with me telling my parents in 3rd grade that; ” I

am going to pursue research after completion of my university studies”. Without much

knowledge of which area to work in or a complete image of what research is all about at

such young age, of course, the travel began to reach this pre-set vision of mine. As the

years of education went by, the area of statistics came to my attention. After my master

degree I got the opportunity to start a doctoral program at Stockholm School of

Economics at the department of Economic Statistics. There I had the privilege of having

a great professor, Anders Westlund, teaching me the path of research. The last year of a

doctoral program has been spent at Aarhus University, School of Business under the

lead of yet another great professor, Kai Kristensen.

There are a lot of people to whom I am very grateful and owe so much

gratitude towards. First of all I would like to mention my husband for being my solid

rock and enabling me time and support at every step of the way together with my three

children that has been, and continues to be, an inspiration to me. I would also like to

thank my parents for never losing faith in me and for always offering a shoulder to lean

on. To my friends and co-workers for showing interest and for all your encouragement

and support, I will be forever grateful.

The analytical part would not have been a success without the hands of

especially Dr Johan Parmler and Bettina Damm. My deepest and warmest thanks for all

your time spent on this project, your counsel, and sharp minds. I am forever grateful for

your involvement.

My utmost professional gratitude is directed to the two professors I have

had the honor to get to know and the privilege of having as tutors; Kai Kristensen and

Anders Westlund – I will always be grateful for all your support, wisdom, guidance and

so much more that no words could ever describe. Thank you for showing and guiding

me down a path I will never stop walking!

- 8 -

- 9 -

Introduction

A company’s performance has traditionally been rated from a financial perspective

using measures such as; EBITDA, EBIT, ROCE, cash flow, etc. However, there has

been an increase of supplementing the financial information with performance criteria’s

from an intangible perspective over the last decades (Ittner & Larcker, 1998a; Ittner &

Larcker1998b). The intangible information used for valuation tools are highly focused

on; human capital, brand equity and customer asset. In this thesis, the focus is placed on

the human capital and customer asset,.

One way of rating and assessing the customer asset and human capital is

through satisfaction measurements where data is collected through surveys. Two

frameworks for this procedure is used here; European Performance Satisfaction Index

(EPSI), surveying the customer asset and European Employee Index (EEI), surveying

the human capital (ECSI, 1998; Eskildsen et al., 2004). Both of these frameworks

pursue both national and international customer and employee satisfaction surveys,

respectively, on an annual basis.

The methodology within these frameworks relies on Structural Equation

Models (SEM). Partial Least Squares (PLS) is applied as the common statistical method

(Lohmöller, 1989; Wold, 1985; Fornell & Cha, 1994; Tenenhaus, et al., 2005; Vilares,

et al., 2005). SEM together with PLS in satisfaction measurements, as within EPSI and

EEI, is based on several authors’ arguments on PLS showing several advantages in

comparison to the covariance based methods (Chin, 1998; Fornell & Bookstein, 1982).

Two argued advantages are that PLS is robust against multicollinearity and non-

normality in data (Cassel, et al., 1999; 2000; and 2001).

However, even though earlier research has implied PLS being robust,

there are still angles to be further viewed within this area. One angle could be to study

to a higher extent, the levels of multicollinearity being present in survey data. Yet

another angle is the fact that most rarely multicollinearity stands alone as an implication

in analysis such as in a context being described here. Non-normality is very much

- 10 -

(highly) present in data as well. These occurrences of matters in empirical applications

are quite common among other things.

Therefore there are still gaps in exploring these empirically seen

implications. This is why chapter 1 and 2 has a theoretical focus placed on i)

multicollinearity and ii) non-normality, in a simplified context of customer satisfaction

measurements aligned with the EPSI model. In chapter 1, the area of interest is

multicollinearity. The study will introduce multicollinearity in two ways, i) within, i.e.

introducing correlations between indicators, also called manifests, on chosen levels and

ii) between, i.e. specifying pre-determined levels of correlations between exogenous

latent variables being present in the model. Moving into chapter 2, the focus is firstly on

introducing non-normality on different levels both in the manifests as well as within the

structural residuals. Secondly a study will be conveyed by introducing a combination of

non-normality together with multicollinearity in the analytical set-up. By analysing a

combination of empirically, common statistical implication should give even more

insight as too how robust PLS is. The first two chapter’s analytical set-up will be

undertaken by the use of Monte-Carlo simulations and the attention will be placed on

the structural parameters in evaluating robustness of PLS in the estimation process.

Continuing into chapter 3, this part evaluates a further enhancement of

leadership in an Employee Engagement context, based on the well-known EEI model.

In the EEI model there are seven established drivers for employee satisfaction, where

Senior Management (SM) and Immediate Manager (IM) are two factors being specified

as exogenous latent variables, i.e. drivers of employee satisfaction. Earlier empirical

findings have shown that the leadership dimensions do not seem to have an extended,

direct, effect on employee satisfaction. However, since many theories within the area of

business excellence has a focus on leadership as ‘drivers’ it seems rather straight

forward to explore this more empirically in a context of employee satisfaction (EFQM,

2011; Shingo Prize, 2011; Baldridge, 2009-2010). The empirical data being analysed in

this study originates from the annual European Employee Index survey, more

specifically data collected in 22 countries globally within the years of 2007-2010. The

main area of interest is the structural parameters between the two leadership dimension

and the five defined drivers of employee satisfaction in the EEI model. This will be

- 11 -

evaluated following a PLS estimation in a re-arranged EEI model (described under

chapter 3). More specifically the effects will be further evaluated by studying the

relative effect in between the two leadership dimensions on the five remaining drivers

of employee satisfaction within the framework of EEI.

Defining structures of data is a common interest in many sciences and

within the area of employee satisfaction measurements it is highly interesting to be able

to segregate between the employees in the estimation process in order to secure an even

better platform for improvement work in every part of the organisation, which is one of

the most important step for any organisation conducting an employee survey, i.e. to find

concrete and actionable improvement areas to work with in a follow-up process.

There are methods from the family of multivariate techniques, with the

aim of ‘grouping’ data, what could be related to the term ‘clustering’, within specified

data sets; FIMIX-PLS, REBUS-PLS, factor analysis and PLS to mention some. Deeper

understanding to these methods could be found in, for instance, Bollen (1989), Jöreskog

(1979a), Jöreskog (1970), Hair et al., (1998) Trinchera (2007); Vinzi et al., (2008),

Ringle et al. (2007), Tenenhaus, et al. (2005) and Vilares, et al. (2005). Being able to

classify employees has a positive effect seen from the perspective of employee

satisfaction measurements, meaning we increase an understanding of their differences

as well as their similarities. This could be done, for instance by adding in knowledge

from demographical or organisational settings in the estimation process in a context

being described under chapter 3, i.e. a context of employee engagement by use of PLS

in estimating a framework such as EEI. When adding in knowledge from sources, not

directly evident in data used for estimation, in such a context would give further added

value in understanding the behaviour and preferences among the employees in the

analytical results received in a set-up being presented in this dissertation. Earlier

research has shown especially demographical differences, which gives some evidence

as to why it could be appropriate to discuss results in a context as the one described here

(Deaux & Major, 1987; Clark et al., 1996; Eskildsen, et al., 2003). However, the

question is if it could be possible to go even deeper in the quest of increasing

knowledge regarding behaviour and preferences in an employee engagement context?

- 12 -

Myer Briggs Type Indicator (MBTI) is a method supposed to categorize

people into different types and profiles depending on people’s preferences from a

psychological perspective and also how people perceive the world and make their

decisions (Carr et al., 2011; Hirsh & Kummerow, 1989). There are other forms for type

classification such as JTI and CPI for instance (Budd, 1993; Gough & Bradley, 1996).

MBTI relies on typological theory of Jung (Jung, 1923).

Chapter 4 will analyse data from 2011 years’ European Employee Index

survey. The ordinary question scheme in the EEI survey was supplemented with four

questions, assumed to follow the MBTI approach. The aim of this study is to analyse the

possibility of finding any differences in impact structure, i.e. structural parameters,

depending on type or profile according to the MBTI, when conducting a PLS analysis in

an employee engagement context by applying the EEI framework. This will be

evaluated by dividing the survey data according to pre-defined answering scheme of the

four specific questions assumed to be related to the MBTI. If possible to combine

knowledge from, for instance MBTI, in evaluating analytical results from an Employee

Engagement survey, could enhance both the understanding of groups of employees,

challenges in different parts of an organisation together with an even more enhanced

opportunity for the further improvement work inside an organisation.

- 13 -

CHAPTER 1: SEM-based customer satisfaction measurement;

On multicollinearity and robust PLS estimation

Westlund, A.H., Källström, M. & Parmler, J. (2008) SEM Based Customer Satisfaction

Measurement; On Multicollinearity and Robust PLS Estimation. Total Quality

Management and Business Excellence, 19(7-8), 855-869.

- 14 -

- 15 -

1.1 Introduction

Systems for performance measurement often play a key role for companies when

developing strategic plans, and when evaluating the achievement of organisational

objectives. Traditionally, the companies have almost exclusively relied on financial

performance measures, such as EBIT, EBITDA, ROCE, cash flow, etc. However, the

understanding of the significance of non-financial information, as well as the use of

non-financial performance measurements, such as human capital, brand equity, the

customer asset, and environmental performance, as additional valuation tools to the

financial performance measurements, has increased over the recent years (Ittner &

Larcker, 1998a, 1998b). Organisations have also seen the value of supplementing the

financial measures with frameworks with which they are able to study several non-

financial performance measures simultaneously. An example of this is the well-known

Balanced Scorecard (Kaplan & Norton, 1996; Banker, et al., 2004).

A possible way of assessing the value of the customer asset is through

customer satisfaction measurements. This is true, in particular, if customer satisfaction

measurements are implemented with structural models, where consequences from

changes in customer satisfaction are rated. In order to secure comparability and

consistency between organisations, national (or even international) measurement

standards are needed. So called national customer satisfaction indices here play an

important role. The scope of conducting national customer satisfaction surveys has

widened, and since the beginning of the 1990’s several countries have developed

national indicators measuring customer satisfaction across a wide range of industries,

companies and organisations. For example, Sweden was the first nation to establish a

national index of customer satisfaction in 1989 (Fornell, 1992); other nations that have

developed national indices are, for example, Norway, (Andreassen & Lindestad, 1998),

Denmark, (Martensen, et al., 2000), and the US with the American Customer

Satisfaction Index (ACSI) (Fornell, et al., 1996). The European Performance

Satisfaction Index (EPSI Rating), (ECSI, 1998), conducts annually harmonised

customer satisfaction surveys for several industries and in an increasing number of

European countries. The EPSI Rating was first initialized by the EC (European

- 16 -

Commission) and the Pan-European quality organisations EFQM (European Foundation

for Quality Management) and EOQ (European Organisation for Quality) in 1997.

The main parts, or the core of the national customer satisfaction models,

are in most ways standardised. However, some differences in the modelling can be seen

(Johnson et al., 2001). Part of the standard is the basic structure which is based on

research in areas of consumer behaviour, customer satisfaction and quality aspects (both

product and service quality), and theories that are well established (Fornell, 1992, 2007;

Fornell et al., 1996). The methodology often relies on a Structural Equation Model

(SEM). For example, a structural model is used within the EPSI Rating to measure and

evaluate customer satisfaction. Within the framework of EPSI Rating, Partial Least

Squares (PLS) is applied as the common statistical method. Alternatives to PLS are

covariance-based methods such as LISREL and Neural Network (Hackl & Westlund,

2000). The use of PLS in customer satisfaction measurement has grown over recent

years, and many authors argue that PLS shows several advantages in comparison to the

covariance-based methods (Chin, 1998; Fornell & Bookstein, 1982). The hypothesis of

PLS being robust against statistical quality problems such as data skewness, antecedent

multicollinearity and mis-specified structural models, are strong reasons for applying

PLS in customer surveys, since the occurrence of such problems in empirical

applications is quite common (Cassel et al, 1999, 2000, 2001). Some authors also argue

that the multicollinearity problem might not be a big obstacle in SEM estimation, with

the estimation being robust against multicollinearity (Malhotra et al., 1999).

The purpose of this paper is to analyse to what extent there will be effects

on the structural parameter estimates from multicollinearity, when applying a PLS

approach for models similar to those used within the EPSI Rating.

- 17 -

1.2 Partial Least Squares

Herman Wold was the first to formalise the main ideas of Partial Least Squares (PLS) in

a paper discussing principal component analysis (Wold, 1966). Other references on the

PLS algorithm are, for example, Wold (1975, 1982, 1985).

PLS is sometimes seen as a ‘soft modeling’ technique, mainly because the

alternative SEM-ML (Jöreskog, 1970), or covariance-based SEM, requires heavier

distributional assumptions. The estimates from using a covariance-based method are

consistent, but when the assumptions of multivariate normal distribution, large sample

size and independence of observations are violated (Bollen, 1989), the covariance-based

methods may produce improper solutions, for example, negative variance (Fornell &

Bookstein, 1982; Chin, 1998). However, PLS estimates are only ‘consistent at large’

which means that the bias of estimates from a PLS procedure will tend to zero, only as

the number of indicators (per block) and sample size increase simultaneously.

To pursue PLS estimation one needs (i) the measurement model, (ii) the

structural model, and (iii) the weight relations. The measurement models relate the

observable manifest variables, or indicators, to directly unobservable latent variables

(unobservable constructs, or factors). The latent variables are denoted ξ (exogenous)

and η (endogenous). The structural model describes the relations between a vector of

endogenous latent variables and a vector of exogenous latent variables (1.1):

ζΓξΒηη (1.1)

where Β and Γ are impact parameter matrices, and ζ is a vector of error terms, where

.}{ 0ξζE (1.2)

- 18 -

The unobservable latent variables are all described by blocks of observable variables x

and y through measurement models. Those models are either reflective, formative or

follow the MIMIC (multiple effect indicators for multiple causes) approach.

The reflective measurement model is given by (1.3) and (1.4) (the

manifest variables are reflections of the latent variables):

xx εξλx (1.3)

yy ελy (1.4)

where E( ξ )= ξm , Var( ξ )=1 and E( η )= m ,Var( η )=1. Furthermore, Wold introduces

the so called ‘predictor specification condition’ as in (1.5) and (1.6):

ξλξx x}{E (1.5)

ηληy y}{E (1.6)

This implies that the residual terms xε and yε have a zero mean and are uncorrelated

with their respective latent variable, i.e. 0)( ξ,ε xCorr and 0)( η,ε yCorr

Formative measurement models are given by

ξξ δxπξ (1.7)

ηη δyπη (1.8)

- 19 -

where the latent variables ξ andη are linear functions of its manifest variables plus a

residual term. The predictor specification condition also holds for the formative

specification.

The weight relations are used to estimate scores or case-values of the

latent variables, as weighted averages of the manifest variables:

ywη η

^

(1.9)

xwξ ξ

^

(1.10)

The weights ξw and ηw are estimated in different ways, depending on the type of

measurement model used (for example, by Mode A or Mode B). For more details on

the PLS algorithm, see, for example, Lohmöller (1989); Wold (1985); Fornell & Cha

(1994); Tenenhaus et al. (2005); and Vilares et al. (2005).

1.3 Study Design

The purpose of this study is to contribute to our knowledge on the small-sample

distributions of the PLS estimator in particular when multicollinearity is present in the

data. The most effective way to generate such knowledge is through Monte-Carlo

simulations. A shortcoming with that approach is the difficulty to generalise

conclusions beyond the study design chosen. Thus, a second purpose is to validate PLS

for estimation, in particular, within the EPSI Rating framework, with a study design

taking characteristics from EPSI Rating. As a consequence, the model set-up and the

parameter specification in the simulation have been specified by examining real survey

data from the EPSI Rating.

- 20 -

The main focus is to study the effects on the PLS estimates of the

structural parameters, when introducing multicollinearity in the data. The correlations

are introduced in two ways: (i) between exogenous latent variables, and (ii) between

indicators.

The structural model used by the EPSI Rating for conducting customer

satisfaction surveys is given in Figure 1.1. The model consists of seven latent variables.

The five on the left – Image, Expectation, Product Quality, Service Quality, and Value -

are seen as the antecedents of variables on the right-hand side; customer satisfaction and

loyalty, the last one being a consequence of customer satisfaction. Each latent variable

is measured by multiple manifests.

Figure 1.1. The EPSI Rating structural model

The data used for the parameter set-up are taken from the Swedish part of

the EPSI Rating, and more specifically from measurements on Retail Banking (B2C)

within the 2006 survey. In Sweden, annual surveys are conducted in approximately 25-

30 industries in the Swedish market (in the private sector as well as the public sector).

These surveys started in 1989 as the Swedish Customer Satisfaction Barometer and

since 1997 are part of the EPSI Rating initiative.

Image

Expectation

Perceived

Product

Quality

LoyaltyCustomer

SatisfactionValue

Perceived

Service

Quality

- 21 -

The structural models in the simulations are simplified versions of the

EPSI Rating model (see Figures 1.2-1.3). Model I consists of 4 latent variables; two

exogenous variables and two endogenous variables with links from each exogenous

variable to both of the endogenous variables. Model II has four exogenous variables and

two endogenous with corresponding links from each of the exogenous variables. A link

between the endogenous variables is also introduced in Model II. The correlations

between the exogenous variables are represented by curved lines.

Figure 1.2. Simulation Model I

A sample of approximately 1.500 observations has randomly been chosen

from the database of the 2006 survey for retail banking in order to set the structural

parameters in the simulation models. Since the simulation models are simplified

versions of the EPSI Rating model, only empirical data for part of the seven latent

variables has been used. For Model I, Product Quality and Service Quality are

exogenous variables, and corresponds to 1ξ and 2ξ , respectively. For Model II, Image

and Expectations are used as exogenous variables ( 3ξ and 4ξ ). Value for Money and

Customer Satisfaction correspond to the two endogenous variables of the simulation

models ( 1 and 2 , respectively).

Perceived

Product

Quality

Customer

Satisfaction

Value

Perceived

Service

Quality

- 22 -

Figure 1.3. Simulation Model II

The measurement models for i , i = 1, 2, 3, 4 follows the formative specification (1.7)

where the error terms are uniformly distributed. The measurement model for 1 and 2

is reflective (1.3-1.6) and, again, the error terms are uniformly distributed.

The inner relations for Model I-II are given by (1.1), where:

2221

12110

II

ΓB

24232221

14131211

21 0

00

IΙIIΓB

which are specified by using empirical data.

Perceived

Product

Quality

Customer

Satisfaction

ValuePerceived

Service

Quality

Image

Expectation

- 23 -

The focus of the study, as mentioned earlier, aims at analysing the effects

of introducing multicollinearity in the measurement process. To do this, first a baseline

model is used (Case A), where the data is assumed to be ‘perfect’ from a statistical point

a view. It is specified without any multicollinearity, and the manifests for the exogenous

latent variables are assumed to be Beta(6,6) distributed.

There will be four manifests for each latent variable. They are all

measured on a 1 to 10 scale, which is standard within the EPSI framework. The

manifest variables for the exogenous latents i (i=1,2,3,4) have all been generated with

a Beta(6,6) distribution. The weights ix were all set to be 1/4. The ij were taken from

the empirical data and were, in Model I, set to be 0.7, 0.5, 0.5 and 0.3 for i = 1,2 and j =

1,2. In Model II, the corresponding ij are specified as 0.5, 0.1, 0.3, 0.3, 0.25, 0.5, 0.1

and 0.1, for i=1,2; j=1,2,3,4 and 21 =0.5. The iy are always set to be 0.75 for i = 1,2…,

8. All error variances are set such that the degrees of explanation ( 2R ) are

approximately 0.65, for sample size n = 250.

The sample size is varied on four levels (n= 100, 250, 500 and 1000). The

case of n= 250 is most consistent with the situation within the EPSI Rating

(approximately 250 observations per company are measured). The other sample sizes

are arbitrarily on lower and higher levels. The number of replications in the simulations

is set to be 1000.

Multicollinearity is introduced in two ways. In Case B we will analyse the

effects of introducing multicollinearity between blocks, i.e. when pre-setting collinearity

between the exogenous factors. The levels of correlation (Corr) will be set on four

levels for both Model I and Model II (0.5, 0.7, 0.9, 0.95). In that sense this is an

extension of the study by Cassel et al. (1999), where the levels of correlation between

the exogenous factors were either 0 or 0.7. The correlations are here introduced by a

Cholesky transformation and a correlation matrix R , specified below. The correlation

matrix has been specified as follows.

- 24 -

1

1

1

1

23

2

2

32

R

where is a parameter between 0 and 1.

This specification has the effect that the correlation between two

neighbouring variables within the same block is . When correlation between the

exogenous latents is introduced, the same principle has been used, i.e. the correlation

between two neighbouring -variables is .

In Case C, collinearity within an exogenous block is introduced (i.e.

between the manifests of an exogenous variable). We restricted ourselves to collinearity

between the manifests of the first exogenous variable. The different levels of

correlations are taken from real-life data. The degree of correlation is calculated by a

variance inflation factor, VIF. In both models (Model I and II) VIF=4, 10, 20, 30 and 50.

VIF

VIF = 4 0.6325

VIF = 10 0.7906

VIF = 20 0.8771

VIF = 30 0.9129

VIF = 50 0.9449

- 25 -

The correlations matrices are of size M x M, i.e. quadratic matrices, and then the VIF

can be calculated as in (1.11).

MMM 122 12 ))()((VIF (1.11)

The simulations are evaluated by examining the RMSE, bias, and variance of all

estimators (over the 1000 replicates).

1.4 Results

Tables 1.1-1.3 show the simulation results for the estimation of the inner

relation parameters for Model II, and for Cases A (base case), B and C. The tables show

the estimated parameters, the estimated RMSE, and the proportion of RMSE originating

from the variance of the estimator. The results are given for the smallest (n=100) and

largest (n=1000) sample sizes used in the simulation process.

Our presentation focuses first on Case A. Table 1 shows that PLS provides

very good estimation of the inner structural parameters Β and Γ . The estimated

differences between the true and estimated parameter values are, in most cases, very

small. This overall picture holds for the smaller sample size n=100, and just minor

improvements are observed with increasing sample size. Results for n=250 and n=500

are available from the authors on request.

- 26 -

Table 1.1: True and estimated parameters in Model II; for Case A, B, and C.

The corresponding RMSEs are small (see Table 1.2). Further reduction in RMSE is

noticed when the sample size increases. The RMSE component is, for most parameters,

dominated by the variance component (see Table 1.3), although the relative variance

contribution is reduced with larger sample sizes. That is expected, as PLS is not

consistent, but just consistent at-large.

Parameter

True

parameter

Case A

(n=100/n=1000)

VIF 0/Corr 0.0 0.5 0.7 0.9 0.95 4 10 20 30 50

0.50.41/

0.48

0.49/

0.57

0.57/

0.63

0.63/

0.69

0.65/

0.71

0.66/

0.66

0.70/

0.70

0.72/

0.72

0.73/

0.73

0.75/

0.73

0.10.00/

0.04

0.05/

0.10

0.10/

0.14

0.15/

0.19

0.17/

0.20

0.01/

0.05

0.01/

0.06

0.01/

0.06

0.00/

0.06

0.00/

0.06

0.30.22/

0.29

0.26/

0.31

0.21/

0.27

0.11/

0.17

0.07/

0.12

0.17/

0.25

0.16/

0.23

0.16/

0.23

0.15/

0.22

0.14/

0.22

0.30.15/

0.20

0.19/

0.22

0.15/

0.19

0.08/

0.11

0.04/

0.08

0.12/

0.19

0.12/

0.18

0.12/

0.18

0.12/

0.18

0.13/

0.18

0.250.18/

0.24

0.11/

0.20

0.11/

0.15

0.07/

0.08

0.04/

0.05

0.15/

0.20

0.14/

0.19

0.14/

0.19

0.13/

0.19

0.13/

0.18

0.50.29/

0.36

0.15/

0.23

0.11/

0.17

0.04/

0.08

0.03/

0.05

0.26/

0.34

0.25/

0.33

0.25/

0.33

0.24/

0.33

0.24/

0.33

0.10.06/

0.06

0.03/

0.04

0.03/

0.02

0.00/

0.01

0.01/

0.01

0.05/

0.05

0.05/

0.05

0.05/

0.05

0.05/

0.05

0.05/

0.05

0.10.02/

0.05

0.00/

0.02

0.01/

0.01

0.00/

0.01

0.00/

0.00

0.03/

0.05

0.03/

0.04

0.03/

0.04

0.02/

0.04

0.02/

0.04

0.50.57/

0.50

0.70/

0.62

0.74/

0.67

0.76/

0.72

0.76/

0.73

0.63/

0.55

0.65/

0.57

0.66/

0.58

0.67/

0.58

0.67/

0.59

VIF

Estimated parameter

Case B

(n=100/n=1000)

Case C

(n=100/n=1000)Corr

11

21

12

22

13

23

14

24

21

- 27 -

Table 1.2: The estimated RMSE of PLS estimates in Model II; for Case A, B, and C.

ParameterCase A

(n=100/n=1000)

VIF 0/Corr 0.0 0.5 0.7 0.9 0.95 4 10 20 30 50

0.15/

0.03

0.15/

0.08

0.13/

0.13

0.17/

0.19

0.18/

0.21

0.16/

0.16

0.21/

0.20

0.23/

0.22

0.24/

0.23

0.25/

0.23

0.12/

0.07

0.09/

0.02

0.06/

0.05

0.08/

0.09

0.10/

0.10

0.13/

0.05

0.14/

0.05

0.14/

0.05

0.14/

0.05

0.14/

0.05

0.15/

0.03

0.13/

0.02

0.14/

0.04

0.22/

0.13

0.24/

0.19

0.17/

0.06

0.17/

0.07

0.17/

0.08

0.18/

0.08

0.19/

0.08

0.17/

0.11

0.13/

0.08

0.16/

0.11

0.23/

0.19

0.26/

0.22

0.19/

0.12

0.19/

0.12

0.20/

0.12

0.20/

0.12

0.19/

0.12

0.13/

0.03

0.18/

0.06

0.17/

0.10

0.20/

0.17

0.23/

0.21

0.14/

0.05

0.13/

0.06

0.14/

0.07

0.14/

0.07

0.14/

0.07

0.24/

0.14

0.36/

0.27

0.40/

0.33

0.46/

0.42

0.47/

0.45

0.27/

0.16

0.28/

0.17

0.28/

0.17

0.28/

0.17

0.28/

0.18

0.09/

0.05

0.10/

0.07

0.11/

0.09

0.13/

0.10

0.12/

0.10

0.09/

0.06

0.09/

0.06

0.09/

0.06

0.09/

0.06

0.08/

0.06

0.11/

0.06

0.12/

0.08

0.11/

0.09

0.12/

0.10

0.12/

0.10

0.10/

0.06

0.11/

0.06

0.10/

0.06

0.11/

0.06

0.11/

0.06

0.11/

0.02

0.21/

0.13

0.25/

0.18

0.27/

0.22

0.27/

0.23

0.17/

0.06

0.19/

0.07

0.20/

0.08

0.20/

0.09

0.20/

0.09

RMSE

Case C

(n=100/n=1000)

Case B

(n=100/n=1000)

VIFCorr

11

21

12

22

13

23

14

24

21

- 28 -

Table 1.3: Percentage Variance in RMSE ( 100 x VarMSE%Variance ij1

ij

)( ijijγ ) in Model II;

for Case A, B, and C.

In Case B, correlations between exogenous latents are introduced, the differences

between the true and estimated parameters are affected (see Table 1.1), but although the

cases of quite extreme multicollinearity are introduced, the effects are rather moderate.

This overall picture is supported by the estimated RMSEs in Table 1.2. The bias part of

RMSE is, for most cases here, substantially higher compared with Case A.

When assuming correlations between manifests (Case C) for one of the exogenous

variables ( 1ξ ), the estimated parameters are, in most cases, almost un-affected (see

Table 1.1). For just one structural parameter ( 11γ ), the effects are more substantial. This

picture holds for the smallest sample size used in the simulation study (n=100), and the

ParameterCase A

(n=100/n=1000)

VIF 0/Corr 0.0 0.5 0.7 0.9 0.95 4 10 20 30 50

57.9/

59.0

99.9/

7.7

71.8/

2.3

38.1/

0.7

29.0/

0.6

11.2/

1.1

5.6/

0.6

3.8/

0.5

3.2/

0.5

2.5/

0.4

36.0/

11.4

70.0/

98.5

100.0/

17.2

66.8/

4.2

50.4/

3.3

48.0/

22.3

53.4/

27.3

57.0/

28.5

52.1/

29.1

51.2/

31.6

69.0/

73.8

89.8/

93.8

57.8/

31.2

25.0/

3.3

13.9/

2.5

39.6/

12.3

36.5/

8.8

31.6/

7.1

29.4/

7.3

27.1/

6.121.9/

4.2

25.2/

5.6

17.2/

2.4

6.5/

0.8

4.1/

0.6

18.7/

3.5

16.3/

3.3

16.6/

3.1

16.7/

3.0

16.6/

2.9

74.5/

74.3

39.3/

14.3

33.5/

5.8

17.2/

2.2

13.4/

2.0

51.1/

16.3

38.0/

11.0

34.8/

9.0

31.6/

8.9

28.2/

8.2

22.0/

2.6

5.8/

0.5

3.2/

0.3

1.6/

0.2

1.0/

0.3

20.0/

2.0

18.4/

1.7

18.1/

1.5

18.0/

1.4

18.5/

1.676.9/

46.6

56.0/

17.7

50.9/

10.7

34.6/

8.0

39.7/

8.2

70.7/

30.2

70.6/

25.9

69.2/

25.1

69.0/

24.3

70.1/

22.551.1/

25.1

31.2/

5.7

28.7/

3.3

21.3/

1.9

21.3/

1.8

52.6/

19.5

53.6/

18.0

53.6/

18.1

46.8/

18.3

43.6/

17.655.8/

98.9

11.9/

2.7

5.6/

1.2

5.0/

0.6

4.9/

0.5

35.4/

23.0

53.6/

18.0

33.8/

12.0

28.5/

10.3

26.3/

11.0

Percentage VAR

Case C

(n=100/n=1000)

Case B

(n=100/n=1000)

VIFCorr

11

21

12

22

13

23

14

24

21

- 29 -

deviations between correct and estimated parameters are almost the same irrespective of

sample size.

As a consequence, the RMSEs are mostly rather small (see Table 1.2), with some

reductions when increasing the sample size. The bias part of RMSE is, in some cases,

higher than in Case A, but as for Case B the picture is rather mixed. The bias part,

however, increases substantially when increasing n (although where relative changes

have a small magnitude).

Overall, the results for Model I appear to be similar to those in Model II (for the results,

see Tables A1.1-A1.3 in the Appendix).

1.5 Conclusions

The purpose of this study was to contribute to our knowledge on the small-sample

distributions of the PLS estimator and evaluate the effects on inner relations of

Structural Equation Models when introducing multicollinearity. This was done through

Monte Carlo simulation.

The multicollinearities introduced in our simulations are substantial, and

normally of higher magnitude than is empirically observed in the EPSI Rating. In spite

of that, PLS estimation shows a very good robustness, in particular with respect to

variance effects. Some increased bias is noticed, but not even the most extreme cases of

multicollinearity ( =0.95, and VIF=50) reduce the quality of estimates beyond what

could be empirically accepted.

As in all Monte-Carlo simulations, the result in this study is limited to the

specific models used for data generation. Therefore, several extensions are

recommended: (i) examine the effects of introducing multicollinearity between

manifests for more than one exogenous latent; (ii) study multicollinearity effects in PLS

when the manifests are skewed (which is empirically motivated); (iii) comparing PLS

with covariance-based methods, for example LISREL, to evaluate the robustness in

comparison with other multivariate methods.

- 30 -

- 31 -

Appendix A1: Simulation results for Model I

Table A1.1: True and estimated parameters in Model I; for Case A, B, and C.

Table A1.2: The estimated RMSE of PLS estimates in Model I; for Case A, B, and C.

Parameter

True

parameter

Case A

(n=100/n=1000)

VIF 0/Corr 0.0 0.5 0.7 0.9 0.95 4 10 20 30 50

0.70.44/

0.48

0.52/

0.58

0.55/

0.61

0.61/

0.64

0.60/

0.65

0.66/

0.66

0.70/

0.70

0.73/

0.72

0.73/

0.73

0.74/

0.73

0.50.37/

0.41

0.45/

0.50

0.48/

0.53

0.52/

0.56

0.52/

0.56

0.58/

0.59

0.63/

0.63

0.67/

0.65

0.65/

0.66

0.67/

0.66

0.50.24/

0.34

0.16/

0.26

0.13/

0.20

0.08/

0.10

0.04/

0.06

0.19/

0.29

0.18/

0.28

0.18/

0.27

0.20/

0.27

0.16/

0.26

0.30.16/

0.25

0.11/

0.19

0.08/

0.15

0.06/

0.07

0.01/

0.04

0.13/

0.22

0.13/

0.21

0.14/

0.20

0.14/

0.20

0.13/

0.20

Estimated parameter

Case B

(n=100/n=1000)

Case C

(n=100/n=1000)Corr VIF

11

21

12

22

Parameter

Case A

(n=100/n=1000)

VIF 0/Corr 0.0 0.5 0.7 0.9 0.95 4 10 20 30 50

0.28/

0.22

0.21/

0.12

0.18/

0.09

0.11/

0.06

0.13/

0.05

0.07/

0.05

0.05/

0.01

0.06/

0.02

0.05/

0.03

0.06/

0.03

0.17/

0.09

0.12/

0.03

0.10/

0.04

0.07/

0.06

0.09/

0.07

0.10/

0.09

0.14/

0.13

0.18/

0.15

0.16/

0.16

0.18/

0.16

0.30/

0.16

0.36/

0.25

0.38/

0.30

0.43/

0.41

0.47/

0.44

0.34/

0.21

0.34/

0.23

0.33/

0.23

0.32/

0.24

0.36/

0.24

0.18/

0.06

0.22/

0.11

0.24/

0.15

0.25/

0.23

0.30/

0.26

0.20/

0.08

0.20/

0.10

0.19/

0.10

0.19/

0.10

0.19/

0.10

RMSE

Case B

(n=100/n=1000)

Case C

(n=100/n=1000)

Corr VIF

11

21

12

22

- 32 -

Table A1.3: Percentage Variance in RMSE ( 100 x VarMSE%Variance ij1

ij

)( ijijγ ) in Model I;

for Case A, B, and C.

Parameter

Case A

(n=100/n=1000)

VIF 0/Corr 0.0 0.5 0.7 0.9 0.95 4 10 20 30 50

14.2/

0.8

24.8/

2.1

31.2/

4.2

41.2/

8.9

43.4/

11.1

59.6/

11.6

100.0/

96.9

64.6/

44.2

74.8/

19.4

53.5/

19.1

38.7/

9.2

83.2/

99.1

96.9/

48.0

90.5/

16.5

94.7/

15.1

30.0/

7.8

13.8/

3.0

10.0/

1.4

8.3/

1.8

9.5/

1.2

21.6/

3.5

12.7/

1.7

5.9/

1.3

4.9/

1.6

3.6/

0.9

15.4/

1.7

12.3/

1.4

8.8/

1.0

10.3/

1.4

9.8/

0.942.7/

18.3

26.6/

5.1

19.0/

3.3

14.3/

3.0

9.0/

2.0

31.8/

6.9

28.2/

6.0

26.4/

6.4

26.9/

5.2

21.3/

6.2

Percentage VAR

Case B

(n=100/n=1000)

Case C

(n=100/n=1000)

Corr VIF

11

21

12

22

- 33 -

1.6 References

Andreassen, T.W. & Lindestad, B. (1998) The effects of corporate image in the

formation of customer loyalty. Journal of Service Marketing, 1(1), 82-92.

Banker, R. D., Chang, H. & Pizzini, M. J. (2004) The balanced scorecard: judgemental

effects of performance measures linked to strategy. The Accounting Review, 79(1), 1-23.

Bollen, K. A. (1989) Structural Equations with Latent Variables, New York: Wiley.

Cassel, C., Hackl, P., & Westlund, A.H. (1999) PLS for estimating latent variable

quality structures: finite sample robustness properties, Journal of Applied Statistics,

26(4), 435-446.

Cassel, C., Hackl, P., & Westlund, A.H. (2000) On measurement of intangible assets: a

study of robustness of partial least squares. Total Quality Management, 11(7), 897-907.

Cassel, C., Eklöf, J, Hackl, P. & Westlund, A.H. (2001) Structural analysis and

measurement of customer perceptions, assuming measurement and specification errors.

Total Quality Management, 12(7-8), 873-881.

Chin, W.W. (1998) Commentary: issues and opinion on structural equation modelling.

MIS Quarterly, 22, pp. vii-xvi.

ECSI (1998) European Customer Satisfaction Index – Foundation and Structure for

harmonized National Pilot Projects. Report prepared by ECSI Technical Committee.

ECSI Document no. 005 ed. 1.

Fornell, C. (1992) A national customer satisfaction barometer: the Swedish experience.

Journal of Marketing, 56(1), 6-21.

Fornell, C. (2007) The Satisfied Customer. New York: Palgrave Macmillan.

- 34 -

Fornell, C. & Bookstein, F.L. (1982) Two structural equation models: LISREL and PLS

applied to consumer exit-voice theory. Journal of Marketing Research, 19(4), 440-452.

Fornell, C. & Cha, J. (1994) Partial least squares. In: R.P.Bagozzi (Ed.) Advanced

Methods in Marketing Research (pp.52-78). Cambridge, MA: B. Blackwell.

Fornell, C., Johnson, M. D., Anderson, E. W., Cha, J., & Everitt Bryant, B., (1996) The

American customer satisfaction index. Nature, purpose, and findings. Journal of

Marketing, 60(4), 7 – 18.

Hackl, P. & Westlund, A.H. (2000) On structural equation modeling for customer

satisfaction measurement. Total Quality Management, 11(4-6), 820-825.

Ittner, C.D. & Larcker, D.F. (1998a) Innovations in performance measurements: Trends

and research implications. Journal of Management Accounting Research, 10, 205-238.

Ittner, C.D. & Larcker, D.F. (1998b) Are nonfinancial measures leading indicators of

financial performance? An analysis of customer satisfaction, Journal of Management

Accounting Research, 36, Studies on Enhancing the Financial Reporting Model, 1-35.

Johnson, M. D., Gustafsson, A., Andreassen, T. W., Lervik, L.& Cha, J. (2001) The

evolution and future of national customer satisfaction index models. Journal of

Economic Psychology, 22(2), 217 – 245.

Jöreskog, K.G. (1970) A general method for analysis of covariance structures.

Biometrika, 57(2), 239-251.

Kaplan, R. S. & Norton, D. (1996) The Balanced Scorecard. Boston: Harvard

University Press.

Lohmöller, J-B (1989) Latent Variable Path Modeling with Partial Least Squares.

Heidelberg: Physica.

- 35 -

Malhotra, N.K., Peterson, M. & Kleiser, S.B. (1999) Marketing research: a state-of-the-

art review and directions for the twenty-first century. Academy of Marketing Science,

27(2), 160-183.

Martensen, A., Gronholdt, L. & Kristensen, K. (2000) The drivers of customer

satisfaction and loyalty: cross-industry findings from Denmark. Total Quality

Mangement, 11(4-6), 544-553.

Tenenhaus, M., Vinzi, V. E., Chatelin, Y-M. & Lauro, C. (2005) PLS path modeling.

Computational Statistics and Data Analysis, 48(1), 159 – 205.

Vilares, M.J., Almeida, M.H. & Coelho, P.S. (2005) Comparison of likelihood and PLS

estimators for structural equation modelling. A simulation with customer satisfaction

data. Technical Report. New University of Lisbon.

Wold, H. (1966) Estimation of principal components and related models by iterative

least squares. In: P.R. Krishnaiah (Ed.), Multivariate Analysis (pp. 391 – 407). New

York: Academic Press.

Wold, H. (1975) Soft modeling by latent variables: the non-linear iterative partial least

squares approach, in J. Gani (Ed.) Perspectives in Probability and Statistics, Papers in

Honour of M. S. Bartlett. London: Academic Press.

Wold, H. (1982) Soft modeling: The basic design and some extensions. In K.G Jöreskog

& H. Wold (Eds.), Systems under indirect observation: Causality, structure, prediction

(Vol. 2, pp. 1-54). Amsterdam: North Holland.

Wold, H. (1985) Partial Least Squares. In: S. Kotz & N. Johnson (Eds), Encyclopedia of

Statistical Sciences (Vol. 6, pp. 581 – 591). New York: Wiley.

- 36 -

- 37 -

CHAPTER 2: Robustness in PLS estimation: Analysing the

effects of introducing Non-normality and

Multicollinearity in Customer Satisfaction Measurement

Data

Mari Källström

Stockholm School of Economics, Aarhus University

- 38 -

2.1 Introduction

Performance measurements and information are high priority areas within organisations.

The most common performance measures have a focus on financial performance

indicators such as ROI (Return on Investment) and ROS (Return on Sales). However

the use of non-financial performance information, or intangible assets, such as the

human capital and the customer asset, has grown and also the value of non-financial

performance measurements has widened. (Ittner & Larcker, 1998a; 1998b).

Organisations of today often evaluate their growth and prospects in terms of a

combination of financial (tangible) and non-financial (intangible) information. In 1992,

the Balanced Scorecard was introduced to provide organisations with a framework for

selecting multiple performance measures, not only focusing on the tangible information

but also supplementing with intangible information (Banker et al., 2004; Kaplan &

Norton, 1996).

Customer measures are intended to measure the organisational

performance from the customer’s perspective. When evaluating the customer asset, a

common strategy is to use customer satisfaction measurements. Sweden was the first

country to develop and establish a national index of customer satisfaction in 1989

(Fornell, 1992) and since the beginning of the 90´s several nations has developed

national indicators measuring consumer satisfaction across a wide range of industries,

companies and organisations (Andreassen & Lindestad, 1998; Martensen et al., 2000;

Fornell et al., 1996). European Performance Satisfaction Index (EPSI Rating) is a non-

profit organisation that has widened the scope of conducting consumer satisfaction

measurements by placing it more on a European level with harmonized customer

satisfaction surveys over several industries and in an increasing number of European

countries (ECSI, 1998). This makes it possible to have a “common currency” when the

interest also lies at performing benchmark between companies, industries, countries as

well as over time.

A common methodology within customer satisfaction measurements is to

use Structural Equation Models (SEM). These models are presumed to give information

on cause and effect relations between the antecedents and consequences of customer

- 39 -

satisfaction imposed in the models. The processes described with a structural model are

also assumed to generate measures of association among the variables depicted in the

model (Williams et al., 2003). The well-established theories which underlies the basic

structure of structural models used in the area of customer satisfaction as well as years

of research within areas such as consumer behaviour and customer satisfaction give

strength to the methodology used (Fornell, 1992; Fornell et al., 1996; and Fornell, 2007)

SEM is also the methodology used within EPSI Rating when measuring

and evaluating customer satisfaction. Within the framework of EPSI Rating the

common statistical method used is Partial Least Squares (PLS), which is a variance-

based multivariate method. Many authors argue that PLS shows several advantages in

comparison with covariance-based methods such as LISREL, EQS and AMOS. These

advantages have contributed to the increasing application of PLS over the recent years

(Chin, 1998; Fornell & Bookstein, 1982). Another alternative to PLS is Neural Network

based SEM, which shows some similarities to PLS but also some distinctions, for

instance Neural Network based techniques in SEM has the possibility to perform

simultaneous measures in the approximation process (Hackl & Westlund, 2000; Hsu et

al., 2006).

The hypothesis of PLS being robust against statistical quality aspects such

as multicollinearity, miss-specified structural models and non-normality (i.e. skewness

in the data), which are also empirical issues common in customer satisfaction studies,

shows strong evidence in favour of using PLS (Cassel et al., 1999; 2000; and 2001,

Westlund et al., 2008). However, the research within the area of studying statistical

aspects of PLS, such as the statistical quality aspects mentioned above, more

theoretically, still faces some gaps.

The aim of this study is to analyse to what extent there would be effects

on the structural parameter estimates when firstly introducing non-normality in the data

and secondly when in combination with non-normality also introduce multicollinearity

in the data, when applying a PLS approach for a model similar to the structural model

used within the framework of EPSI Rating.

- 40 -

2.2 Estimation Procedure

The estimation of Structural Equation Models faces some difficulties such as; i) the

latent variables are not observed, ii) the manifest variables that correspond to responses

on a questionnaire from a customer satisfaction survey may (highly) likely not follow a

normal distribution and skewness to the right on the scale is more common, iii) the

occurrence of multicollinearity on some levels are often present. The two families of

methods commonly used to estimate these types of structural models are covariance-

based methods and variance-based methods, i.e. PLS.

PLS is seen as a “soft modelling” technique. The reason is that PLS can be

seen as a distribution free method, since there is no need of any assumptions regarding

the distribution of the manifest variable, or about the independence of observations.

This in comparison with SEM-ML, covariance based SEM, also known as “Hard

modelling," which has stronger distributional assumptions and several hundreds of cases

are necessary (Jöreskog, 1970). The estimates from using a covariance-based method

are consistent, but when the assumptions of multivariate normal distribution, large

sample size and independence of observations are violated, the covariance-based

methods may produce improper solutions, for example negative variance (Fornell &

Bookstein, 1982; Chin 1998). However, PLS estimates are only “consistent at large”

which means that the bias of estimates from a PLS procedure will tend to zero only as

the number of latent variables (per block) and sample size increase simultaneously.

Covariance-based methods will not be a part of this study, so the

estimation process will not be discussed here. The author refers to the numerous

literatures discussing the different techniques further; see for example Jöreskog (1970);

Boomsma et al. (2001) and Hsu et al. (2006).

The first to formalize the idea of Partial Least Squares was Herman Wold

in a paper discussing principal component analysis (Wold, 1966).

To pursue PLS estimation you need i) the measurement model, ii) the

structural model, and iii) the weight relations. The measurement model (or outer model)

relates the manifest variables, or indicators (observable constructs), to pre-specified

- 41 -

latent variables (unobservable constructs). The latent variables are defined as ξ andη ,

depending on if the latent variable is exogenous ( ξ ) or endogenous ( η ). The structural

model (or inner model) describes the relations between some endogenous latent

variables with other latent exogenous variables. This is denoted as in (2.1):

ζΓξΒηη (2.1)

where Β and Γ are impact parameter matrices, and ζ is a vector of error terms, where

.}{ 0ξζE (2.2)

Since the latent variables are unobservable they are all individually described by a block

of observable variables x and y. The ways of relating the indicators to their respective

latent variable are threefold; the reflective one, the formative way and the MIMIC

(multiple effect indicators for multiple causes) approach.

The reflective measurement model is given by (2.3) and (2.4) (the

manifest variables are reflections of the latent variables):

xx εξλx (2.3)

yy ελy (2.4)

where E( ξ )= ξm , Var(ξ )=1 and E( η )= m ,Var( η )=1. Furthermore, a hypothesis to be

fulfilled, introduced by Wold, is the so called “predictor specification condition” as in

(2.5) and (2.6):

- 42 -

ξλξx x}{E (2.5)

ηληy y}{E (2.6)

This implies that the residual terms xε and yε have a zero mean and are uncorrelated

with their respective latent variable, i.e. 0)( ξ,ε xCorr and 0)( η,ε yCorr

Often a more appropriate way for the exogenous variables will be to use a

formative specification of the relations. If the exogenous latent variable/-s is supposedly

generated by its own manifest variables then it is called a formative model for ξ .

Formative measurement models are given by;

ξξ δxπξ (2.7)

ηη δyπη (2.8)

where the latent variables ξ and η are linear functions of its manifest variables plus a

residual term. The predictor specification condition also holds for the formative

specification.

The general definition of the weight relations is that they are used to

estimate scores or case-values of the latent variables, as weighted averages of the

manifest variables:

ywη η

^

(2.9)

xwξ ξ

^

(2.10)

- 43 -

Estimation of the weights ξw and

ηw are twofold, Mode A and Mode B, depending on

if the measurement model follows a reflective or formative approach. For more details

on the PLS algorithm, see for example, Lohmöller (1989); Fornell & Cha (1994);

Tenenhaus, et al. (2005); and Vilares, et al. (2005).

2.3 Study Design

The purpose of this study is to continue the contribution of the knowledge on small-

sample distributions of the PLS estimator in particular when non-normality and

multicollinearity are present in data. This will be done through Monte Carlo simulations,

due to the complexity of SEM models and PLS, which makes it hard to assess the

robustness in an analytical form. The second purpose is to compare the results in this

analysis with Westlund et al. (2008), where a study on multicollinearity present in data

was undertaken and the impact and robustness on PLS estimation was evaluated. Both

the model set-up and the parameter specifications in the simulation process have been

specified according to Westlund et al. (2008).

The focus of this study is to analyse the effects non-normality have on

PLS estimates of the inner model (structural) parameters. The non-normality will be

introduced as a combination of i) non-normality within the manifest data and ii) non-

normality within the structural residuals. These aspects will be studied simultaneously

in order to examine to what extent the structural parameters will be affected when also

combining the two non-normality perspectives. However, the two criteria’s mentioned

above will also be analysed separately in order to study what the impact will be if only

one of the non-normality issues is present. Another focus will be to introduce

multicollinearity from two perspectives: i) between multicollinearity, i.e. between

exogenous latent variables and ii) within multicollinearity, i.e. within exogenous

variable (between manifests). With this set-up it will be possible to study the combined

effects on the structural parameters when having both non-normality and

multicollinearity present when performing a PLS estimation.

- 44 -

The structural model used in customer satisfaction surveys by EPSI Rating

consists of seven latent variables, where the first five are seen as driving factors (Image,

Expectation, perceived Product Quality, perceived Service Quality and Value) and the

other two, Customer Satisfaction and Loyalty, are seen as the resulting (performance)

factors in the model. Each latent variable is measured by multiple manifests (Westlund

et al. 2008; ECSI, 1998). The same parameter set-up is used in this study as in Westlund

et al. (2008).

One of the simplified versions of the EPSI Rating model also analysed in

Westlund et al. (2008) will be undertaken in this article. The structural model consists

of 4 latent variables; two exogenous and two endogenous with links from each

exogenous variable to both of the endogenous variables. The correlation between the

two exogenous variables is represented by a curved line (see Figure 2.1).

Figure 2.1 Simulation Model

The two exogenous variables (1ξ and

2ξ ) corresponds to Product Quality

and Service Quality. Value (1 ) and Customer Satisfaction (

2 ) corresponds to the two

endogenous variables.

The measurement models for i , i =1,2, follows the formative

specification (2.7) where the error terms are uniformly distributed. The measurement

model for 1 and

2 is reflective (3-6) and again, the error terms are uniformly

distributed.

The inner relation for the simulation model is given by (2.1), where:

Perceived

Product

Quality

Customer

Satisfaction

Value

Perceived

Service

Quality

- 45 -

2221

12110

ΓB

which are specified as in Westlund et al. (2008).

The focus of the study, as mentioned earlier, aims at analysing the effects

of introducing non-normality in the measurement process and also combining the two

statistical aspects of skewness and multicollinearity and study the effects on PLS

estimation such a set-up has on the inner parameters of a structural model. The base

case, or baseline model in this study, will be where the simulation is specified without

any impact of multicollinearity, the manifest variables of the exogenous variables are

generated from the symmetric beta(6,6) distribution and the structural residuals are

assumed to be normally distributed.

As mentioned earlier the set-up of the parameters in the structural model;

ix , ij and iy will be specified as in Westlund et al. (2008) which means that

ix will

be set to be ¼, ij will be set to be 0.7, 0.5, 0.5 and 0.3 for i = 1,2 and j = 1,2 and iy is

set to be 0.75 throughout the simulation process. All error variances are set such that the

degrees of explanation ( 2R ) are approximately 0.65, for sample size n = 500. The

number of manifests is set to be four in every part of the simulation process. They are

all measured on a 1-10 scale, which is the standard procedure within the EPSI Rating

framework. The sample size will vary on two levels; n=100 and n=500. The number of

replications is set to be 5000.

The first focus will be to study the effects of introducing non-normality as

a combination of two perspectives, namely i) non-normality within the manifests of the

exogenous variables and ii) non-normality within the structural residuals. There will be

16 combinations of non-normality to study on two levels of sample size, which implies

a total of 32 cases of non-normality to analyse.

- 46 -

The non-normality will be introduced by generating both the manifests

and the structural residuals from skewed beta distributions (see Table 2.1). For both the

manifests and the structural residuals an EPSI specific case (*) has been developed by

analysing empirical data from the financial sector from the Swedish part of EPSI

Rating. Empirical data has been analysed over two years (2005 and 2006) in a trial-and-

error environment to be able to match a beta distribution on both the manifests and the

structural residuals. The purpose of the chosen beta distributions is to be able to analyse

i) a symmetrical case (beta(6,6)) ii) moderate non-normality (beta(6,4), beta(6,2)) and

iii) a severe case of non-normality (beta(8.1)).

Table 2.1: Beta distribution for the manifest variables and the structural residuals

The four beta distributions used in this article are depicted in Figure 2.2-

2.5, to show the skewness of the chosen beta distributions graphically.

Figure 2.2. Beta(6,6) distribution Figure 2.3. Beta(6,4) distribution

Design beta (6,6) beta (6,4) beta (6,2)* beta (8,1)N(0, 0.22) "Basecase"

beta (6,4)

beta(7, 3.5)*

beta (8,1)

* EPSI Specific distributions, from the financial sector

Manifest Distribution

Stru

ctu

ral

Res

idu

als

0.20 0.40 0.60 0.80

beta(6,6)

0

25

50

75

100

Co

un

t

0.20 0.40 0.60 0.80

beta(6,4)

0

25

50

75

Co

un

t

- 47 -

Figure 2.4. Beta(6,2) distribution Figure 2.5. Beta(8,1) distribution

The second focus will be to also introduce multicollinearity in

combination with non-normality as specified above. In Westlund et al. (2008)

multicollinearity was analysed in two ways; i) between blocks by setting the levels of

correlation (Corr) on four levels and ii) within the first exogenous block by studying the

Variance Inflation Factor (VIF) on five levels. This approach will be replicated here,

however the levels of Corr in this study will only be set on two levels (0.5 and 0.95) and

the levels of VIF will also be set on two levels (VIF= 10 and 30). The purpose of this is

to be able to study the effects when multicollinearity is introduced on i) a moderate

level and ii) on a more severe level. The introduction of the within block

multicollinearity will be done firstly on the first exogenous latent variable (denoted 1

Ksi under Results) and an extension with this study in comparison to Westlund et al.

(2008) is that the within block multicollinearity will be introduced and studied on both

exogenous variables simultaneously (denoted 2 Ksi under Results).

The correlations are introduced by a Cholesky transformation, as in

Westlund et al. (2008) and the correlation matrix has been specified as follows.

0.40 0.60 0.80

beta(6,2)

0

25

50

75

100

Co

un

t

0.50 0.60 0.70 0.80 0.90

beta(8,1)

0

50

100

150

Co

un

t

- 48 -

1

1

1

1

23

2

2

32

R

where is a parameter between 0 and 1.

This specification has the effect that the correlation between two

neighbouring variables within the same block is . However, it also specifies the

correlation to decrease when increasing the number of manifests. This might induce a

more positive effect on estimation and will be evaluated in the simulation process.

When correlation between the exogenous latents is introduced, the same principle has

been used, i.e. the correlation between two neighbouring -variables is .

VIF

VIF = 10 0.7906

VIF = 30 0.9129

The correlations matrices are of size M x M, i.e. quadratic matrices, and then the VIF

can be calculated as in (2.11). This application follows the same structure as in

Westlund et al. (2008)

MMM 122 12 ))()((VIF (2.11)

- 49 -

The simulations are evaluated by examining the Root Mean Square Error (RMSE), bias,

and variance of all estimators (over the 5000 replicates).

2.4 Results

As described earlier the theoretical model used in this study consists of four latent

variables, two exogenous and two endogenous. The presentation of the results from the

simulation study undertaken is threefold.

Tables 2.2-2.4 show the simulation results when non-normality is present;

both when skewness is present between the manifest variables as well as within the

structural residual.

Tables 2.5-2.7 show the simulation results when a combination of non-

normality, as described above and multicollinearity is introduced between the

exogenous latent variables, when pre-setting the levels of correlation on two levels,

denoted Corr, in the tables.

The last part of the result presentation consists of Tables 2.8a-2.10b. Here

the results from the simulation process are presented, where a combination of non-

normality and multicollinearity between the manifest variables are present in the data,

when pre-setting the level of within multicollinearity on two levels using VIF.

Tables 2.2-2.10 show the estimated parameters, the estimated RMSE, and

the proportion of RMSE originating from the variance of the estimator in each case. The

results are presented for the two levels of sample sizes being analysed; n=100 and

n=500.

PLS is a biased multivariate method, i.e. it is not consistent, but consistent

at large. The consensus of this is that the bias in the estimation process will decrease as i)

the model increases in terms of increasing the number of manifests per latent variable

and ii) the sample size increases. In this study the focus has been on increasing the

- 50 -

sample size and not to increase the number of manifests at any stage of the simulation

process.

When examining the basecase in Table 2.2, the parameter estimates are

good, even on the smaller sample size. This is mainly due to the large number of

replicates used in this simulation. Improvements in estimation can be seen when

increasing the sample size, which is also expected. Despite the lack of non-normality

the estimates are negatively biased. This is related to the fact that PLS is only consistent

at large and is yet another confirmation to the theoretical aspect of PLS. These findings

are in line with the results found in Westlund et al. (2008).

- 51 -

Table 2.2: True and estimated parameters; when non-normality is present in the data and

structural residuals.1

1 Set up of inner structural model distribution as in Westlund et al. (2008).

*Basecase

**EPSI specific case

ParameterTrue Parameter

Value Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1)

0.7 100 0.42* 0.44 0.44 0.27

500 0.47* 0.50 0.49 0.37

0.5 100 0.36* 0.39 0.38 0.24

500 0.41* 0.43 0.41 0.31

0.5 100 0.27* 0.28 0.28 0.14

500 0.33* 0.35 0.34 0.24

0.3 100 0.18* 0.18 0.20 0.12

500 0.23* 0.25 0.24 0.17

0.7 100 0.53 0.54 0.54 0.36

500 0.57 0.58 0.58 0.57

0.5 100 0.51 0.52 0.52 0.34

500 0.54 0.56 0.55 0.54

0.5 100 0.34 0.34 0.33 0.22

500 0.38 0.40 0.39 0.38

0.3 100 0.25 0.27 0.26 0.18

500 0.29 0.31 0.31 0.29

0.7 100 0.52 0.53 0.53** 0.37

500 0.55 0.57 0.57** 0.45

0.5 100 0.48 0.50 0.50** 0.35

500 0.51 0.54 0.53** 0.41

0.5 100 0.34 0.35 0.33** 0.21

500 0.38 0.41 0.40** 0.31

0.3 100 0.25 0.28 0.26** 0.16

500 0.30 0.32 0.32** 0.23

0.7 100 0.49 0.49 0.50 0.33

500 0.53 0.55 0.54 0.43

0.5 100 0.46 0.47 0.48 0.33

500 0.50 0.53 0.51 0.40

0.5 100 0.31 0.32 0.30 0.19

500 0.37 0.39 0.38 0.29

0.3 100 0.24 0.26 0.24 0.15

500 0.29 0.31 0.31 0.22

beta(8,1)

Parameter Estimates

(mean value over 5000 replicates)

N(0,0.22)1

Manifest Distributions

beta(6,4)

beta(7, 3.5)

11

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

- 52 -

When the manifests are assumed to follow a moderate beta distribution, no larger effects

can be seen on the parameter estimates compared to basecase. As can be seen in Table

2.3 RMSE shows no distinct effects in any direction and no severe increase in bias are

indicated. This is confirmed by the quite steady levels of variance from Table 2.4. These

findings support the hypothesis of PLS being robust against non-normality in, at least

moderate, manifest distributions.

In the case of introducing severe non-normality in the manifests, larger

effects on the parameter estimates are indicated. The large increase in RMSE is almost

exclusively due to large increase in bias. However, when increasing the sample size the

parameter estimates improve and could also be seen as an indication of PLS being quite

robust even when having severe non-normality within the manifest distribution, a case

which is seldom (or never) seen empirically. The results seem positive with regards to

the robustness of PLS; however a discussion regarding the choice of set-up could also

be interesting to review.

- 53 -

Table 2.3: The estimated RMSE of PLS estimates; when non-normality is present in the data and

structural residuals.

In the case of introducing non-normality in the structural residuals, an interesting

finding is that the estimates improve. An implication that might have an effect is a lack

Parameter Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1)

100 0.30* 0.28 0.28 0.46

500 0.23* 0.21 0.21 0.33

100 0.18* 0.15 0.17 0.29

500 0.10* 0.08 0.10 0.20

100 0.27* 0.26 0.26 0.39

500 0.17* 0.15 0.16 0.26

100 0.17* 0.17 0.16 0.22

500 0.09* 0.06 0.07 0.14

100 0.20 0.18 0.19 0.37

500 0.14 0.12 0.13 0.14

100 0.09 0.10 0.10 0.20

500 0.05 0.07 0.06 0.05

100 0.20 0.20 0.21 0.32

500 0.13 0.10 0.11 0.13

100 0.13 0.11 0.12 0.19

500 0.04 0.04 0.04 0.04

100 0.21 0.20 0.21** 0.36

500 0.15 0.13 0.14** 0.25

100 0.11 0.10 0.13** 0.18

500 0.04 0.05 0.04** 0.10

100 0.21 0.19 0.22** 0.32

500 0.12 0.10 0.11** 0.20

100 0.13 0.11 0.12** 0.20

500 0.04 0.04 0.04** 0.08

100 0.24 0.24 0.23 0.40

500 0.18 0.15 0.16 0.27

100 0.12 0.12 0.12 0.21

500 0.04 0.04 0.04 0.11

100 0.23 0.21 0.24 0.34

500 0.14 0.11 0.12 0.22

100 0.14 0.11 0.13 0.21

500 0.04 0.04 0.04 0.09

beta(7, 3.5)

beta(8,1)

RMSE

(mean value over 5000 replicates)

N(0,0.22)

Manifest Distributions

beta(6,4)

11

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

- 54 -

of controlling for 0}{ ξζE in the simulation process. However, the level of parameter

estimates are quite steady when increasing the non-normality in the structural residuals.

This together with the findings of lowered RMSE and an increase in variance, which

indicates decreased bias effects, still gives some evidence of robustness. But the

shortcoming mentioned indicates that further research should be undertaken, since no

further evaluation of this has been undertaken here.

- 55 -

Table 2.4: Percentage Variance in RMSE ( 100 x VarMSE%Variance ij1

ij

ijγ ); when non-

normality is present in the data and structural residuals.

Both the theoretical model used as well as the parameter set-up originates from the

EPSI framework. Even the distribution of manifests and structural residuals has been

Parameter Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1)

100 11.5* 16.5 15.5 12.1

500 1.8* 2.3 2.1 1.4

100 34.2* 44.7 47.5 17.9

500 15.5* 20.9 15.2 5.0

100 25.9* 26.0 25.1 13.6

500 7.2* 5.0 5.9 4.8

100 47.7* 51.9 58.5 30.9

500 30.9* 30.8 35.8 13.9

100 22.8 25.1 28.7 13.7

500 5.0 5.5 4.2 5.0

100 98.2 95.6 97.2 34.8

500 43.2 19.3 37.2 43.2

100 34.1 37.7 33.0 22.3

500 8.4 10.1 10.5 8.4

100 82.2 92.8 88.4 56.7

500 93.7 89.8 97.6 93.7

100 23.2 25.4 32.8** 12.9

500 4.8 4.3 3.71** 2.4

100 98.1 99.9 99.9** 34.0

500 88.5 36.4 64.8** 14.4

100 36.2 37.7 35.5** 20.9

500 10.5 12.2 12.5** 3.9

100 85.9 95.4 90.3** 53.1

500 99.9 74.3 87.8** 27.4

100 22.3 24.8 26.0 13.6

500 3.6 3.2 2.7 2.0

100 90.5 95.2 97.0 35.6

500 99.3 57.9 88.9 14.5

100 31.7 31.6 30.7 18.2

500 8.3 9.1 10.6 3.9

100 78.2 88.2 82.1 50.7

500 96.0 85.5 98.7 22.7

beta(8,1)

Percentage VAR

(mean value over 5000 replicates)

N(0,0.22)

Manifest Distributions

beta(6,4)

beta(7, 3.5)

11

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

- 56 -

tested in comparison with empirical data from EPSI, where an EPSI specific case has

been identified. This case is interesting to discuss since this has an empirical link to the

simulations undertaken. Compared to basecase, the EPSI specific case yields better

estimates (see Table 2.2). RMSE decreases (Table 2.3), which is mainly due to the

increased variance effects as can be confirmed in Table 2.4. This implies further that the

bias effects are in some way decreased. These results support the hypothesis of PLS

being robust against non-normality in cases which, at least, are empirical evident.

Table 2.5: True and estimated parameters; A combination of when i) non-normality is present in

the data and structural residuals and ii) multicollinearity is introduced between the exogenous

latent variables.

ParameterTrue Parameter

Value Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1)

0.7 100 0.52 0.55 0.55 0.36 0.60 0.63 0.63 0.44

500 0.57 0.60 0.59 0.46 0.65 0.68 0.66 0.52

0.5 100 0.45 0.48 0.47 0.31 0.51 0.55 0.54 0.37

500 0.49 0.52 0.50 0.38 0.56 0.59 0.57 0.43

0.5 100 0.18 0.17 0.18 0.10 0.04 0.03 0.04 0.02

500 0.24 0.26 0.25 0.17 0.04 0.05 0.05 0.03

0.3 100 0.11 0.12 0.13 0.07 0.02 0.01 0.03 0.01

500 0.17 0.19 0.18 0.13 0.03 0.04 0.04 0.03

0.7 100 0.61 0.63 0.63 0.45 0.67 0.70 0.70 0.52

500 0.65 0.67 0.66 0.53 0.72 0.74 0.73 0.59

0.5 100 0.59 0.60 0.60 0.42 0.64 0.67 0.66 0.48

500 0.62 0.64 0.62 0.48 0.67 0.70 0.68 0.53

0.5 100 0.22 0.22 0.19 0.13 0.04 0.04 0.04 0.03

500 0.27 0.29 0.28 0.21 0.05 0.06 0.06 0.04

0.3 100 0.16 0.18 0.17 0.11 0.03 0.03 0.03 0.03

500 0.21 0.23 0.23 0.16 0.04 0.05 0.05 0.03

0.7 100 0.61 0.63 0.62** 0.45 0.67 0.70 0.70** 0.52

500 0.64 0.66 0.66** 0.53 0.71 0.74 0.72** 0.59

0.5 100 0.56 0.58 0.58** 0.43 0.62 0.66 0.65** 0.49

500 0.59 0.62 0.61** 0.48 0.66 0.69 0.67** 0.53

0.5 100 0.21 0.22 0.20** 0.12 0.04 0.04 0.04** 0.03

500 0.27 0.29 0.29** 0.21 0.05 0.07 0.06** 0.04

0.3 100 0.16 0.18 0.17** 0.09 0.03 0.04 0.04** 0.02

500 0.22 0.24 0.23** 0.17 0.04 0.05 0.05** 0.03

0.7 100 0.57 0.59 0.59 0.41 0.64 0.67 0.67 0.48

500 0.61 0.64 0.63 0.50 0.68 0.71 0.69 0.56

0.5 100 0.55 0.57 0.57 0.40 0.62 0.65 0.65 0.48

500 0.58 0.61 0.60 0.47 0.66 0.69 0.67 0.54

0.5 100 0.20 0.20 0.19 0.13 0.04 0.04 0.05 0.03

500 0.26 0.28 0.27 0.19 0.05 0.06 0.06 0.04

0.3 100 0.15 0.17 0.16 0.10 0.04 0.03 0.04 0.02

500 0.22 0.23 0.23 0.16 0.04 0.05 0.05 0.03

beta(7, 3.5)

beta(8,1)

Manifest Distributions - Corr 0.95

Parameter Estimates

(mean value over 5000 replicates)

N(0,0.22)

Manifest Distributions - Corr 0.5

beta(6,4)

Parameter Estimates

(mean value over 5000 replicates)

11

21

12

22

11

21

12

22

11

21

12

22

21

12

22

11

- 57 -

In the case of introducing moderate beta distributions on the manifests,

only slight improvements are noticeable, regardless of structural residual distribution or

sample size.

However, in the more extreme case of non-normality (beta(8,1)), the

effects are more severe. From Table 2.6 and Table 2.7 it is evident that the

corresponding RMSE:s, in comparison with basecase, decrease when introducing

between block multicollinearity, however the variance proportion is much higher

especially when n is low (see Table 2.7).

Table 2.6: The estimated RMSE of PLS estimates; A combination of when i) non-normality is

present in the data and structural residuals and ii) multicollinearity is introduced between the

exogenous latent variables.

Parameter Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1)

100 0.20 0.18 0.18 0.38 0.14 0.11 0.10 0.29

500 0.13 0.11 0.12 0.25 0.06 0.03 0.04 0.18

100 0.11 0.09 0.10 0.23 0.10 0.09 0.10 0.18

500 0.04 0.04 0.03 0.13 0.07 0.09 0.08 0.08

100 0.35 0.35 0.34 0.42 0.46 0.47 0.47 0.48

500 0.26 0.24 0.25 0.33 0.46 0.45 0.45 0.47

100 0.22 0.21 0.20 0.26 0.30 0.30 0.28 0.30

500 0.14 0.12 0.13 0.18 0.27 0.27 0.26 0.28

100 0.13 0.10 0.11 0.28 0.10 0.06 0.04 0.21

500 0.05 0.04 0.04 0.17 0.03 0.05 0.21 0.12

100 0.12 0.13 0.13 0.13 0.17 0.18 0.19 0.10

500 0.12 0.14 0.13 0.04 0.18 0.20 0.10 0.05

100 0.30 0.30 0.33 0.39 0.47 0.47 0.45 0.47

500 0.23 0.21 0.22 0.30 0.45 0.44 0.47 0.47

100 0.18 0.16 0.18 0.23 0.28 0.28 0.26 0.29

500 0.10 0.08 0.09 0.15 0.27 0.25 0.29 0.27

100 0.14 0.11 0.12** 0.27 0.10 0.07 0.07** 0.21

500 0.07 0.04 0.05** 0.17 0.03 0.04 0.03** 0.11

100 0.12 0.12 0.13** 0.12 0.16 0.17 0.17** 0.09

500 0.10 0.12 0.05** 0.04 0.16 0.19 0.17** 0.05

100 0.31 0.31 0.33** 0.40 0.46 0.46 0.46** 0.47

500 0.23 0.21 0.22** 0.29 0.45 0.44 0.44** 0.46

100 0.19 0.16 0.18** 0.25 0.28 0.27 0.27** 0.29

500 0.09 0.07 0.08** 0.14 0.26 0.25 0.26** 0.27

100 0.17 0.15 0.15 0.32 0.12 0.08 0.08 0.25

500 0.09 0.07 0.08 0.20 0.03 0.02 0.02 0.14

100 0.12 0.12 0.12 0.15 0.16 0.17 0.17 0.10

500 0.09 0.11 0.10 0.05 0.16 0.19 0.17 0.05

100 0.33 0.32 0.34 0.39 0.47 0.47 0.46 0.48

500 0.24 0.22 0.23 0.31 0.46 0.44 0.44 0.47

100 0.20 0.16 0.18 0.23 0.28 0.28 0.28 0.29

500 0.09 0.08 0.09 0.15 0.27 0.25 0.25 0.27

beta(7, 3.5)

beta(8,1)

RMSE

(mean value over 5000 replicates)

Manifest Distributions - Corr 0.95

N(0,0.22)

Manifest Distributions - Corr 0.5

beta(6,4)

RMSE

(mean value over 5000 replicates)

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

11

- 58 -

Increasing the level of multicollinearity to 0.95 increases the bias effect substantially for

example in 12 and

22 , so that the variance proportion is nearly negligible. The

opposite pattern is shown for example in 11 and

21 , where the variance proportion in

RMSE seems to increase in most cases.

Table 2.7: Percentage Variance in RMSE ( 100 x VarMSE%Variance ij1

ij

ijγ ); A combination of

when i) non-normality is present in the data and structural residuals and ii) multicollinearity is

introduced between the exogenous latent variables.

When introducing more severe beta distribution (beta(8,1)) the effects are more severe.

The estimates decrease, however improvements are seen both with regards of increasing

n and also when increasing the level of multicollinearity. The corresponding RMSE:s in

Table 2.6 and the proportion of variance explained in RMSE in Table 2.7 show no clear

Parameter Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1)

100 20.9 28.7 27.7 17.1 49.7 59.9 54.1 20.0

500 4.9 7.0 5.6 2.2 20.9 49.8 30.2 3.4

100 75.8 94.3 92.9 30.2 99.0 71.1 78.4 45.5

500 94.9 71.8 99.9 10.6 23.3 8.3 18.1 25.8

100 14.1 13.8 12.0 7.5 3.0 2.6 3.8 2.5

500 3.8 2.8 3.7 3.6 1.0 1.1 1.1 0.9

100 26.4 25.5 31.6 21.3 11.3 7.6 9.5 10.4

500 14.8 10.5 14.9 9.4 3.0 2.1 2.8 2.7

100 51.3 56.1 58.4 17.7 93.6 99.8 100.0 24.2

500 24.6 43.7 27.7 3.6 61.1 17.8 32.6 7.0

100 52.7 37.8 42.8 61.3 33.1 13.2 15.3 95.5

500 6.4 3.2 5.6 72.1 2.3 1.0 2.0 58.2

100 13.4 13.6 16.6 11.3 2.1 2.6 2.7 3.8

500 3.2 3.3 3.6 2.8 1.1 1.1 1.1 0.7

100 40.9 39.8 42.6 30.6 8.7 7.2 8.9 9.9

500 19.5 23.0 28.3 11.2 2.9 2.5 3.6 2.1

100 51.5 56.1 61.5** 17.6 92.7 100.0 99.9** 23.6

500 19.9 29.8 22.1** 4.1 85.3 22.7 42.7** 7.9

100 72.5 50.2 62.4** 63.8 41.5 16.4 22.7** 97.8

500 8.9 4.1 7.1** 72.5 2.5 1.3 2.2** 50.8

100 15.7 14.1 15.4** 11.1 2.4 2.9 2.9** 3.3

500 3.8 3.7 4.2** 2.7 1.1 1.3 1.3** 0.7

100 42.8 42.9 42.2** 29.9 9.5 6.9 8.3** 9.9

500 22.7 25.1 31.7** 11.1 2.9 2.6 4.3** 2.4

100 40.9 43.2 46.8 16.7 73.4 82.7 82.4 20.0

500 10.6 13.0 10.1 3.2 60.1 92.2 93.5 5.3

100 83.7 67.0 69.1 59.2 44.7 20.9 21.0 94.5

500 12.1 4.7 8.5 68.0 2.9 1.1 2.2 50.0

100 13.7 12.5 14.9 7.8 2.2 3.1 3.0 3.3

500 3.3 3.2 4.2 2.8 1.2 1.3 1.3 0.7

100 40.7 37.5 41.8 27.2 9.3 6.6 8.8 11.2

500 20.9 23.1 31.1 11.4 3.0 2.6 3.9 2.1

beta(7, 3.5)

beta(8,1)

Percentage VAR

(mean value over 5000 replicates)

Manifest Distributions - Corr 0.95

N(0,0.22)

Manifest Distributions - Corr 0.5

beta(6,4)

Percentage VAR

(mean value over 5000 replicates)

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

11

- 59 -

overall pattern, however in most cases the increase in the RMSE:s seems to a higher

extent be originating from bias effects.

In the case of introducing multicollinearity within the exogenous variables

(between manifests), the results reveal that when setting the level of VIF on 10 and

focusing only on the first exogenous variable (1 Ksi) the estimates improve compared

with basecase, however this is only seen for 11 and

21 (Table 2.8a.).

Table 2.8a: True and estimated parameters; A combination of when i) non-normality is present in

the data and structural residuals and ii) multicollinearity is introduced within the manifest

variables when VIF=10, only on the first exogenous variable (1 Ksi) and in both exogenous

variables (2 Ksi).

ParameterTrue Parameter

Value Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1)

0.7 100 0.69 0.72 0.71 0.58 0.64 0.65 0.66 0.54

500 0.70 0.72 0.71 0.59 0.64 0.66 0.66 0.56

0.5 100 0.62 0.65 0.65 0.50 0.59 0.61 0.61 0.48

500 0.63 0.66 0.64 0.51 0.60 0.62 0.61 0.49

0.5 100 0.21 0.20 0.20 0.14 0.46 0.48 0.47 0.39

500 0.27 0.28 0.27 0.21 0.46 0.47 0.47 0.40

0.3 100 0.14 0.14 0.14 0.11 0.35 0.38 0.37 0.31

500 0.19 0.20 0.20 0.15 0.35 0.36 0.36 0.30

0.7 100 0.78 0.79 0.79 0.66 0.70 0.71 0.72 0.61

500 0.79 0.80 0.79 0.67 0.72 0.73 0.72 0.63

0.5 100 0.75 0.76 0.76 0.62 0.70 0.71 0.72 0.59

500 0.75 0.77 0.75 0.63 0.70 0.72 0.71 0.60

0.5 100 0.23 0.23 0.20 0.18 0.49 0.51 0.51 0.45

500 0.28 0.30 0.29 0.25 0.48 0.49 0.49 0.45

0.3 100 0.17 0.18 0.16 0.14 0.40 0.43 0.42 0.37

500 0.23 0.24 0.23 0.19 0.40 0.41 0.41 0.35

0.7 100 0.77 0.79 0.79** 0.66 0.70 0.71 0.72** 0.61

500 0.77 0.79 0.78** 0.68 0.70 0.71 0.71** 0.63

0.5 100 0.74 0.76 0.75** 0.62 0.69 0.70 0.71** 0.59

500 0.73 0.76 0.74** 0.63 0.69 0.71 0.70** 0.60

0.5 100 0.24 0.23 0.21** 0.17 0.50 0.51 0.51** 0.45

500 0.29 0.31 0.30** 0.25 0.49 0.50 0.50** 0.45

0.3 100 0.18 0.18 0.17** 0.13 0.41 0.43 0.43** 0.36

500 0.23 0.24 0.24** 0.20 0.41 0.42 0.42** 0.36

0.7 100 0.75 0.77 0.76 0.64 0.68 0.69 0.70 0.59

500 0.75 0.77 0.76 0.66 0.68 0.70 0.69 0.61

0.5 100 0.73 0.75 0.74 0.61 0.68 0.69 0.70 0.58

500 0.72 0.75 0.73 0.62 0.68 0.70 0.69 0.59

0.5 100 0.22 0.23 0.20 0.16 0.48 0.50 0.50 0.43

500 0.28 0.30 0.29 0.24 0.48 0.49 0.50 0.43

0.3 100 0.17 0.18 0.16 0.13 0.40 0.43 0.42 0.36

500 0.23 0.24 0.23 0.19 0.40 0.42 0.41 0.35

beta(7, 3.5)

beta(8,1)

Manifest Distributions - VIF 10 (2 Ksi)

Parameter Estimates

(mean value over 5000 replicates)

N(0,0.22)

Manifest Distributions - VIF 10 (1 Ksi)

beta(6,4)

Parameter Estimates

(mean value over 5000 replicates)

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

11

- 60 -

An interesting observation is that the estimates for especially 12γ and 22γ seem to be

improving when introducing multicollinearity within both of the exogenous variables.

The above described pattern is also seen in the case of introducing multicollinearity on

both exogenous variables (see Table 2.8a). This picture also holds when VIF=30 (Table

2.8b). However, a difference seem to be an increase in variance proportions in the

corresponding RMSE:s, see Table 2.9b and Table 2.10b. The variance proportions are

even more substantial when multicollinearity is introduced on both exogenous variables.

Table 2.8b: True and estimated parameters; A combination of when i) non-normality is present in

the data and structural residuals and ii) multicollinearity is introduced within the manifest

variables when VIF=30, only on the first exogenous variable (1 Ksi) and in both exogenous

variables (2 Ksi).

ParameterTrue Parameter

Value Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1)

0.7 100 0.72 0.74 0.74 0.61 0.66 0.67 0.68 0.57

500 0.73 0.75 0.74 0.62 0.66 0.68 0.67 0.58

0.5 100 0.65 0.68 0.68 0.53 0.62 0.63 0.64 0.50

500 0.66 0.68 0.67 0.54 0.62 0.65 0.63 0.52

0.5 100 0.20 0.19 0.18 0.14 0.47 0.49 0.49 0.41

500 0.25 0.26 0.26 0.20 0.47 0.48 0.48 0.41

0.3 100 0.13 0.13 0.13 0.10 0.36 0.40 0.39 0.32

500 0.18 0.19 0.19 0.15 0.37 0.38 0.38 0.31

0.7 100 0.80 0.81 0.81 0.69 0.72 0.72 0.73 0.63

500 0.81 0.82 0.81 0.70 0.73 0.74 0.73 0.64

0.5 100 0.77 0.79 0.78 0.65 0.71 0.72 0.73 0.61

500 0.77 0.79 0.78 0.65 0.72 0.73 0.72 0.62

0.5 100 0.22 0.21 0.19 0.17 0.50 0.52 0.52 0.47

500 0.27 0.28 0.27 0.24 0.49 0.50 0.50 0.46

0.3 100 0.17 0.16 0.16 0.13 0.41 0.44 0.44 0.38

500 0.22 0.23 0.22 0.18 0.41 0.42 0.42 0.37

0.7 100 0.79 0.81 0.81** 0.70 0.71 0.72 0.73** 0.64

500 0.79 0.81 0.80** 0.71 0.72 0.72 0.72** 0.65

0.5 100 0.76 0.78 0.78** 0.65 0.70 0.71 0.72** 0.62

500 0.76 0.78 0.77** 0.65 0.71 0.72 0.72** 0.62

0.5 100 0.22 0.21 0.19** 0.16 0.51 0.52 0.52** 0.46

500 0.28 0.29 0.28** 0.24 0.50 0.51 0.51** 0.46

0.3 100 0.17 0.17 0.16** 0.12 0.42 0.45 0.44** 0.38

500 0.22 0.23 0.23** 0.19 0.42 0.43 0.43** 0.37

0.7 100 0.77 0.79 0.79 0.67 0.70 0.70 0.71 0.61

500 0.78 0.79 0.79 0.68 0.70 0.71 0.71 0.63

0.5 100 0.75 0.77 0.77 0.64 0.70 0.71 0.72 0.60

500 0.75 0.77 0.76 0.64 0.70 0.72 0.71 0.61

0.5 100 0.21 0.21 0.19 0.15 0.50 0.51 0.51 0.45

500 0.27 0.28 0.27 0.23 0.49 0.50 0.50 0.45

0.3 100 0.16 0.17 0.15 0.12 0.42 0.44 0.43 0.37

500 0.22 0.23 0.22 0.18 0.42 0.42 0.42 0.37

beta(7, 3.5)

beta(8,1)

Manifest Distributions - VIF 30 (2 Ksi)

Parameter Estimates

(mean value over 5000 replicates)

N(0,0.22)

Manifest Distributions - VIF 30 (1 Ksi)

beta(6,4)

Parameter Estimates

(mean value over 5000 replicates)

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

11

- 61 -

The deviations between true and estimated parameters are almost the same irrespective

of sample size. The effect of improved parameter estimates is evident when introducing

moderate beta distributions on the structural residuals, but not when introducing

moderate beta distributions in the manifests. However, the parameters decrease in the

severe case of beta distribution on either the structural residuals or the manifests, but not

as low (a level) as might have been expected.

A consequence of having small deviations between the true and estimated

parameters is that the RMSE:s are mostly rather small (see Table 2.9a). The bias part,

however, increases in most cases substantially when increasing the sample size. This is

yet another confirmation to the findings in Westlund et al. (2008).

Table 2.9a: The estimated RMSE of PLS estimates; A combination of when i) non-normality is

present in the data and structural residuals and ii) multicollinearity is introduced within the

manifest variables when VIF=10, only on the first exogenous variable (1 Ksi) and in both

exogenous variables (2 Ksi).

Parameter Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1)

100 0.05 0.05 0.05 0.14 0.08 0.07 0.06 0.17

500 0.02 0.03 0.02 0.11 0.06 0.04 0.05 0.15

100 0.14 0.16 0.16 0.08 0.11 0.12 0.13 0.08

500 0.13 0.16 0.14 0.03 0.10 0.12 0.11 0.03

100 0.31 0.33 0.32 0.38 0.08 0.07 0.07 0.13

500 0.24 0.23 0.23 0.30 0.05 0.04 0.04 0.11

100 0.19 0.19 0.19 0.22 0.10 0.11 0.10 0.09

500 0.12 0.10 0.11 0.16 0.06 0.07 0.07 0.04

100 0.09 0.10 0.10 0.07 0.05 0.05 0.05 0.11

500 0.09 0.10 0.09 0.04 0.03 0.03 0.03 0.08

100 0.25 0.27 0.26 0.13 0.21 0.22 0.22 0.10

500 0.25 0.27 0.25 0.13 0.20 0.22 0.21 0.10

100 0.29 0.29 0.33 0.34 0.07 0.06 0.06 0.09

500 0.22 0.21 0.21 0.25 0.03 0.03 0.03 0.06

100 0.16 0.15 0.18 0.20 0.12 0.14 0.14 0.11

500 0.08 0.07 0.08 0.11 0.10 0.11 0.12 0.06

100 0.08 0.10 0.10** 0.06 0.05 0.05 0.05** 0.10

500 0.07 0.09 0.08** 0.03 0.02 0.02 0.02** 0.07

100 0.24 0.26 0.26** 0.13 0.19 0.21 0.21** 0.11

500 0.23 0.26 0.25** 0.13 0.19 0.21 0.20** 0.10

100 0.28 0.29 0.32** 0.35 0.07 0.06 0.06** 0.09

500 0.21 0.20 0.21** 0.25 0.03 0.02 0.03** 0.06

100 0.15 0.15 0.17** 0.21 0.13 0.15 0.14** 0.11

500 0.08 0.06 0.07** 0.11 0.11 0.12 0.12** 0.06

100 0.06 0.08 0.08 0.08 0.06 0.05 0.05 0.12

500 0.05 0.07 0.06 0.05 0.03 0.02 0.02 0.09

100 0.23 0.25 0.25 0.12 0.19 0.20 0.20 0.10

500 0.22 0.25 0.23 0.12 0.18 0.20 0.19 0.09

100 0.30 0.29 0.32 0.37 0.07 0.06 0.06 0.10

500 0.22 0.20 0.21 0.27 0.03 0.03 0.03 0.07

100 0.16 0.15 0.18 0.21 0.12 0.14 0.14 0.11

500 0.08 0.07 0.08 0.12 0.11 0.12 0.12 0.06

beta(7, 3.5)

beta(8,1)

RMSE

(mean value over 5000 replicates)

Manifest Distributions - VIF 10 (2 Ksi)

N(0,0.22)

Manifest Distributions - VIF 10 (1 Ksi)

beta(6,4)

RMSE

(mean value over 5000 replicates)

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

11

- 62 -

The estimates improve when setting VIF=10 and increasing the non-normality in both

the structural parameter as well as increasing non-normality in the manifests. Even the

severe case, beta(8,1), the estimates are on an acceptable level, but what is showing is

that in most cases the bias effect increases to a higher extent. The same pattern is shown

regardless of VIF=10 for case 1 ksi as well as in 2 ksi, with a distinction of lowered

RMSE when 2 ksi case is evaluated. This is mainly due to an increase in variance.

Table 2.9b: The estimated RMSE of PLS estimates; A combination of when i) non-normality is

present in the data and structural residuals and ii) multicollinearity is introduced within the

manifest variables when VIF=30, only on the first exogenous variable (1 Ksi) and in both exogenous

variables (2 Ksi).

Increasing the correlation within the exogenous variable for 1 Ksi does not show any

strong effects on the parameter estimates, which still lies on an acceptable level. This

Parameter Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1)

100 0.05 0.06 0.06 0.11 0.07 0.06 0.05 0.15

500 0.03 0.05 0.04 0.08 0.04 0.03 0.03 0.12

100 0.16 0.19 0.18 0.08 0.13 0.14 0.15 0.08

500 0.16 0.19 0.17 0.05 0.13 0.15 0.14 0.03

100 0.31 0.33 0.33 0.38 0.07 0.06 0.06 0.12

500 0.25 0.24 0.25 0.31 0.04 0.03 0.03 0.09

100 0.19 0.19 0.20 0.22 0.10 0.12 0.11 0.09

500 0.13 0.11 0.12 0.16 0.07 0.08 0.08 0.04

100 0.11 0.12 0.12 0.05 0.06 0.05 0.06 0.09

500 0.11 0.12 0.12 0.03 0.04 0.04 0.04 0.06

100 0.27 0.29 0.28 0.16 0.22 0.23 0.23 0.13

500 0.27 0.29 0.28 0.16 0.22 0.23 0.22 0.12

100 0.29 0.32 0.34 0.35 0.06 0.06 0.06 0.08

500 0.24 0.22 0.23 0.26 0.02 0.02 0.03 0.05

100 0.16 0.17 0.18 0.20 0.13 0.15 0.15 0.11

500 0.09 0.08 0.09 0.12 0.11 0.13 0.13 0.08

100 0.10 0.12 0.11** 0.05 0.05 0.05 0.06** 0.08

500 0.10 0.11 0.11** 0.03 0.03 0.03 0.03** 0.06

100 0.26 0.28 0.28** 0.16 0.21 0.22 0.23** 0.13

500 0.26 0.28 0.27** 0.16 0.21 0.22 0.22** 0.12

100 0.30 0.32 0.33** 0.36 0.06 0.06 0.06** 0.08

500 0.23 0.21 0.22** 0.26 0.02 0.03 0.03** 0.05

100 0.17 0.17 0.18** 0.21 0.14 0.16 0.15** 0.12

500 0.09 0.07 0.08** 0.11 0.12 0.13 0.13** 0.08

100 0.08 0.10 0.10 0.06 0.05 0.05 0.05 0.10

500 0.08 0.09 0.09 0.03 0.02 0.02 0.02 0.07

100 0.25 0.27 0.27 0.15 0.20 0.21 0.22 0.12

500 0.25 0.27 0.26 0.15 0.20 0.22 0.21 0.11

100 0.31 0.32 0.33 0.36 0.06 0.05 0.06 0.09

500 0.23 0.22 0.23 0.27 0.02 0.02 0.03 0.06

100 0.17 0.16 0.18 0.21 0.13 0.15 0.15 0.11

500 0.09 0.08 0.09 0.12 0.12 0.13 0.13 0.07

beta(7, 3.5)

beta(8,1)

RMSE

(mean value over 5000 replicates)

Manifest Distributions - VIF 30 (2 Ksi)

N(0,0.22)

Manifest Distributions - VIF 30 (1 Ksi)

beta(6,4)

RMSE

(mean value over 5000 replicates)

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

11

- 63 -

could be seen as a strong confirmation of PLS being very robust when focusing on the

parameter estimate. However, could the set-up have a strong implication to the results

given in this study?

Table 2.10a: Percentage Variance in RMSE ( 100 x VarMSE%Variance ij1

ij

ijγ ); A combination

of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is

introduced within the manifest variables when VIF=10, only on the first exogenous variable (1 Ksi)

and in both exogenous variables (2 Ksi).

Parameter Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1)

100 97.9 89.0 91.0 19.3 44.3 54.0 58.4 14.3

500 99.3 47.1 69.6 6.7 13.8 22.2 19.2 3.8

100 16.5 9.0 13.6 99.8 27.8 17.6 24.6 93.5

500 4.0 2.1 3.0 95.6 6.9 3.4 5.4 91.0

100 12.4 13.9 12.4 8.0 78.7 89.3 81.2 33.4

500 3.5 2.7 3.2 3.8 24.3 38.7 44.9 9.9

100 26.3 25.4 32.4 21.7 71.7 42.8 47.6 99.5

500 15.4 10.3 14.6 10.7 24.0 16.1 21.9 99.5

100 22.3 13.5 16.5 62.4 99.7 95.0 83.4 28.1

500 4.9 2.4 3.0 49.7 55.6 34.6 52.9 10.1

100 2.5 2.3 2.1 16.8 5.9 5.4 4.8 28.2

500 0.5 0.4 0.6 4.3 1.0 0.8 1.3 7.1

100 14.2 12.7 16.4 12.3 98.7 96.7 99.0 71.8

500 2.3 2.4 3.3 2.3 53.3 89.0 96.2 20.5

100 37.7 35.1 40.5 36.0 32.4 15.8 19.7 60.3

500 18.6 20.0 28.5 10.3 6.7 5.7 7.5 21.1

100 27.4 15.8 17.0** 66.6 99.9 97.8 86.7** 29.9

500 8.9 3.1 4.2** 58.0 100.0 72.9 88.1** 11.1

100 3.3 2.7 2.4** 13.8 7.2 6.1 5.5** 25.1

500 0.6 0.4 0.6** 3.3 1.2 0.9 1.4** 5.8

100 13.3 14.6 14.3** 12.3 99.7 95.1 98.8** 67.6

500 3.2 2.6 3.6** 1.9 85.7 99.0 97.3** 17.5

100 38.3 40.0 40.2** 34.4 30.0 14.9 19.5** 67.8

500 23.5 20.7 31.7** 10.3 5.6 4.9 6.0** 18.1

100 45.5 26.1 31.9 41.3 88.5 96.9 99.9 21.3

500 15.6 5.6 6.9 26.3 66.9 97.8 89.8 7.6

100 3.8 3.1 3.1 17.2 8.3 7.0 6.3 30.7

500 0.8 0.5 0.7 3.9 1.4 0.9 1.5 6.5

100 13.1 13.2 14.0 11.8 94.7 99.7 99.7 54.6

500 2.9 2.5 4.1 2.3 60.9 94.4 97.2 14.5

100 37.0 36.4 39.4 33.0 33.3 18.1 19.1 70.9

500 21.4 19.9 32.2 10.1 6.2 5.5 7.5 20.1

beta(7, 3.5)

beta(8,1)

Percentage VAR

(mean value over 5000 replicates)

Manifest Distributions - VIF 10 (2 Ksi)

N(0,0.22)

Manifest Distributions - VIF 10 (1 Ksi)

beta(6,4)

Percentage VAR

(mean value over 5000 replicates)

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

11

- 64 -

Table 2.10b: Percentage Variance in RMSE ( 100 x VarMSE%Variance ij1

ij

ijγ ); A combination

of when i) non-normality is present in the data and structural residuals and ii) multicollinearity is

introduced within the manifest variables when VIF=30, only on the first exogenous variable (1 Ksi)

and in both exogenous variables (2 Ksi).

2.6 Conclusions

The purpose of this study was to continue the contribution of the knowledge on small-

sample distributions of the PLS estimator in particular when non-normality and

multicollinearity is present in the data. This was done through Monte-Carlo simulations.

Both the non-normality criteria’s used as well as the level of

multicollinearity being incorporated, both within block and between blocks, on a

moderate as well as severe levels.

Parameter Sample size

nInner Structural

Modelbeta(6,6) beta(6,4) beta(6,2) beta(8,1) beta(6,6) beta(6,4) beta(6,2) beta(8,1)

100 88.5 46.0 52.9 29.7 59.6 69.2 79.0 17.3

500 35.8 12.2 15.4 11.7 26.5 48.0 45.0 5.2

100 11.3 5.6 8.3 87.9 17.5 11.8 15.6 99.6

500 2.3 1.4 1.8 42.1 3.9 2.4 3.4 79.6

100 11.5 11.6 10.8 7.3 88.6 97.9 94.7 40.3

500 3.1 2.4 3.4 3.7 39.5 59.6 66.7 12.8

100 24.1 24.1 29.5 21.0 58.6 30.5 38.1 93.7

500 13.5 8.8 13.8 10.0 14.2 11.3 15.5 87.4

100 13.8 7.9 9.3 98.3 91.1 82.8 65.3 39.9

500 2.5 1.3 1.7 99.2 25.2 17.8 28.6 18.2

100 2.0 1.6 1.3 9.1 4.8 4.1 4.0 17.7

500 0.4 0.3 0.5 2.7 0.8 0.7 1.2 4.6

100 10.0 14.1 13.3 11.8 99.8 86.0 93.1 82.1

500 2.4 1.9 3.3 2.2 77.4 99.4 99.3 32.8

100 32.9 34.7 35.9 32.6 23.3 12.3 15.8 49.8

500 15.7 14.3 24.4 9.0 4.6 4.4 5.7 14.4

100 17.1 9.0 9.7** 99.5 95.8 88.9 69.1** 41.5

500 4.1 1.6 2.2** 93.4 67.5 35.4 50.7** 19.6

100 2.3 1.8 1.6** 8.1 5.7 4.8 4.5** 16.6

500 0.4 0.3 0.4** 2.1 1.0 0.7 1.1** 4.0

100 12.8 14.8 12.2** 11.7 98.9 82.7 91.8** 80.0

500 2.8 2.2 3.6** 1.8 99.8 84.8 80.0** 28.8

100 34.9 36.9 34.4** 30.9 22.0 11.3 15.5** 54.0

500 17.6 14.1 25.5** 8.7 4.4 3.9 4.7** 13.0

100 26.6 13.0 17.1 72.6 99.1 99.3 91.4 29.3

500 6.3 2.4 3.1 74.7 99.9 71.0 85.7 13.4

100 2.9 2.1 1.9 9.4 6.4 5.4 4.8 19.6

500 0.5 0.3 0.5 2.4 1.0 0.7 1.3 4.3

100 11.9 12.9 11.6 9.6 99.8 92.9 97.4 65.1

500 2.6 2.0 4.2 2.2 90.0 99.2 97.2 20.8

100 33.7 31.5 33.5 29.0 23.9 14.2 15.6 57.5

500 16.5 12.6 27.1 9.6 4.5 4.4 5.7 14.5

beta(7, 3.5)

beta(8,1)

Percentage VAR

(mean value over 5000 replicates)

Manifest Distributions - VIF 30 (2 Ksi)

N(0,0.22)

Manifest Distributions - VIF 30 (1 Ksi)

beta(6,4)

Percentage VAR

(mean value over 5000 replicates)

21

12

22

11

21

12

22

11

21

12

22

11

21

12

22

11

- 65 -

In the case of introducing non-normality, the results imply that PLS is

quite robust against non-normality issues, both when skewness is present in the

manifests variables and also in a combination of also introducing skewness in the

structural residuals. However, in the more severe case of non-normality (beta(8,1)) the

impact on the estimates is more severe. It is also evident that the bias effect increases

substantially when introducing a more severe case of non-normality.

When introducing non-normality in a combination with introducing

multicollinearity between the exogenous variables the estimates improve in some cases,

but two parameters seem to be more affected when especially increasing the level of

multicollinearity. The variance effect increases in most cases, however the bias effect is

more substantial both when increasing the level of multicollinearity and when non-

normality is introduced on a more severe level.

Comparing the results above with the case of combining the aspect of non-

normality with the introduction of multicollinearity within exogenous variable/-s, minor

improvements in the estimates appear. This is also evident when severe non-normality

is introduced. The bias effect becomes more evident when increasing the level of within

multicollinearity but also when having multicollinearity on both exogenous variables.

Looking at the results given in this simulation study the results show that

PLS is very robust on the moderate levels of both non-normality and multicollinearity.

Interesting is also that when severe cases are introduced, PLS still generates estimates

beyond what would be empirically acceptable. At first glance we could give a star to

PLS for its robustness, however a question arises – are the numbers valid? As with all

Monte-Carlo simulations the results and conclusions is only valid for the specific model

generated. To be able to generalize even more the set-up should be evaluated to be even

more similar to empirical situations. There are quite a number of research papers

focusing on PLS and its suitability for satisfaction surveys with regards to both theory

and set-up (Kristensen & Eskildsen, 2010; Nielsen et al., 2009).

What would the effect be on the parameter estimates if a larger model

were to be evaluated? It is very common to look at simplified models (looking at the

tradition), but since this is not the case empirically the researcher emphasize this a bit

- 66 -

more. Would the same pattern, in relation to non-normality and multicollinearity being

introduced, be shown when introducing more complexity with regards to modelling set-

up (i.e. a full EPSI model in this case)?

Another shortcoming might be the correlation set-up used in this research.

The set-up, in this study, implies the correlations to diminish when including more and

more factors, which is highly not likely to be the case in reality. Above implies yet

another research approach to be able to draw even more general conclusions, that is to

use a correlation set-up between the factors more similar to reality, for instance the

suggested set-up presented in Nielsen et al., (2009), where the suggestion is to have at

least the same correlation between the factors, since this is more often seen in empirical

data.

To be able to discuss the positive effect of conducting satisfaction surveys

using PLS as the statistical method instead of other methods on the market, more

comparisons should be undertaken to also be able to compare the robustness, towards

the quality aspects discussed here, between the diversity of multivariate methods.

Some extensions should therefore be in focus; i) examine the effects when

a larger model is introduced, ii) study the correlation effect with situations more evident

empirically and iii) extend the scope of the results with a comparison with more

covariance based methods.

- 67 -

2.7 References

Andreassen, T.W. & Lindestad, B. (1998) The effects of corporate image in the

formation of customer loyalty. Journal of Service Marketing, 1(1), 82-92.

Banker, R. D., Chang, H. & Pizzini, M. J. (2004) The balanced scorecard: judgemental

effects of performance measures linked to strategy. The Accounting Review, 79(1), 1-23.

Boomsma, A. & Hoogland, J.J. (2001) The Robustness of LISREL Modeling Revisited,

in R. Cudeck, S. Dau Toit, D. Sörbom, D. (Ed.), Structural Equation Modeling: Present

and Future, a Festschrift in Honor of Karl Jöreskog (pp. 139-168). SSI Scientific

Software International, Lincolnwood, IL.

Cassel, C., Hackl, P., & Westlund, A.H. (1999) PLS for estimating latent variable

quality structures: finite sample robustness properties, Journal of Applied Statistics,

26(4), 435-446.

Cassel, C., Hackl, P., & Westlund, A.H. (2000) On measurement of intangible assets: a

study of robustness of partial least squares. Total Quality Management, 11(7), 897-907.

Cassel, C., Eklöf, J, Hackl, P. & Westlund, A.H. (2001) Structural analysis and

measurement of customer perceptions, assuming measurement and specification errors.

Total Quality Management, 12(7-8), 873-881.

Chin, W.W. (1998) Commentary: issues and opinion on structural equation modelling.

MIS Quarterly, 22, pp. vii-xvi.

ECSI (1998) European Customer Satisfaction Index – Foundation and Structure for

harmonized National Pilot Projects. Report prepared by ECSI Technical Committee.

ECSI Document no. 005 ed. 1.

Fornell, C. (1992) A national customer satisfaction barometer: the Swedish experience.

Journal of Marketing, 56(1), 6-21.

- 68 -

Fornell, C. (2007) The Satisfied Customer. New York: Palgrave Macmillan.

Fornell, C. & Bookstein, F.L. (1982) Two structural equation models: LISREL and PLS

applied to consumer exit-voice theory. Journal of Marketing Research, 19(4), 440-452.

Fornell, C. & Cha, J. (1994) Partial least squares. In: R.P.Bagozzi (Ed.) Advanced

Methods in Marketing Research (pp.52-78). Cambridge, MA: B. Blackwell.

Fornell, C., Johnson, M. D., Anderson, E. W., Cha, J., & Everitt Bryant, B., (1996) The

American customer satisfaction index. Nature, purpose, and findings. Journal of

Marketing, 60(4), 7 – 18.

Hackl, P. & Westlund, A.H. (2000) On structural equation modeling for customer

satisfaction measurement. Total Quality Management, 11(4-6), 820-825.

Hsu, S-H., Chen, W-H., & Hsieh, M-J. (2006) Robustness Testing of PLS, LSIREL,

EQS and ANN-based SEM for measuring Customer Satisfaction. Total Quality

Management, 17(3), 355-371.

Ittner, C.D. & Larcker, D.F. (1998a) Innovations in performance measurements: Trends

and research implications. Journal of Management Accounting Research, 10, 205-38.

Ittner, C.D. & Larcker, D.F. (1998b) Are nonfinancial measures leading indicators of

financial performance? An analysis of customer satisfaction, Journal of Management

Accounting Research, 36, Studies on Enhancing the Financial Reporting Model, 1-35.

Jöreskog, K.G. (1970) A general method for analysis of covariance structures.

Biometrika, 57(2), 239-251.

Kaplan, R. S. & Norton, D. (1996) The Balanced Scorecard. Boston: Harvard

University Press.

- 69 -

Kristensen, K. & Eskildsen, J. (2010) Design of PLS-Based Satisfaction Studies. In: V.

Esposito Vinzi et al. (Ed.) Handbook of Partial Least Squares (pp. 247-277). Berlin

Heidelberg: Springer Verlag.

Lohmöller, J-B (1989) Latent Variable Path Modeling with Partial Least Squares.

Heidelberg: Physica.

Martensen, A., Gronholdt, L. & Kristensen, K. (2000) The drivers of customer

satisfaction and loyalty: cross-industry findings from Denmark. Total Quality

Mangement, 11(4-6), 544-553.

Nielsen, R. Kristensen, K. & Eskildsen, J.K. (2010) Robustness of PLS path modeling

under conditions common in satisfaction studies, paper presented on the 6th

International Conference on Partial Least Squares and Related Methods, Kina, Beijing

Tenenhaus, M., Vinzi, V. E., Chatelin, Y-M. & Lauro, C. (2005) PLS path modeling.

Computational Statistics and Data Analysis, 48(1), 159 – 205.

Vilares, M.J., Almeida, M.H. & Coelho, P.S. (2005) Comparison of likelihood and PLS

estimators for structural equation modelling. A simulation with customer satisfaction

data. Technical Report. New University of Lisbon.

Westlund, A.H., Källström, M. & Parmler, J. (2008) SEM Based Customer Satisfaction

Measurement; On Multicollinearity and Robust PLS Estimation. Total Quality

Management and Business Excellence, 19(7-8), 855-869.

Williams, L.J., Edwards, J.R. & Vandenberg, R.J. (2003) Recent Advances in Causal

Modeling Methods for Organisational and Management Research. Journal of

Management, 29(6), 903-936.

Wold, H. (1966) Estimation of principal components and related models by iterative

least squares. In: P.R. Krishnaiah (Ed.), Multivariate Analysis (pp. 391 – 407). New

York: Academic Press.

- 70 -

- 71 -

CHAPTER 3: Enhancement of Leadership in Employee

Engagement Modelling

Mari Källström

Aarhus University

- 72 -

3.1 Introduction

Searching the Internet for a definition of a leader gives millions of hits, not surprisingly

since leadership is a wide-spread concept depending on the context for which it is used.

Taking an organisational perspective one definition could be “a person who rules,

guides or inspires others”. The cultural phenomena surrounding leadership, was not

seen as any “big issue” before the middle of 1990 (Dorfman, 1996), but the image of

this has changed. Reviewing research and theory on international leadership imply that

reflections on cultural influences in leadership processes are highly evident (House et al.,

1999; House, 2004; Yukl, 2002).

In an organisation the leaders could be seen as the steering wheel and

employees as the engine – together with the management. Some might argue that

management and leadership are one and the same; however a distinct difference

between these is you manage things and lead people. Depending on the size of a

company, (most) organisations may have different layers of leadership. Looking more

closely at two kinds of leadership highly evident in most organisations i) Top

management, i.e. senior management, having a strategic overview and ii) Immediate

manager/-s having a more operational focus for everyday life in an organisation. The

impact from different levels of leadership on employees is very interesting to measure

and analyse, but it is a context hard to measure directly and needs to be incorporated in

concept.

One perspective where it could be interesting to analyse the effect of

management is with regards to employee satisfaction and loyalty. A reason for this

could be that research has shown that employee satisfaction does have an impact on the

financial results (Kristensen & Westlund, 2004). Learning more about impact from

management towards employee satisfaction from different layers within an organisation

will strengthen the focus even more in organisational development from this perspective.

When evaluating the human capital, a common strategy is to pursue

Employee Satisfaction surveys. A company focusing on leadership from two

perspectives when surveying and analysing employee satisfaction is Ennova. The two

- 73 -

angles are; i) Senior Management (i.e. top management) and ii) Immediate Manager. A

major focus area when conducting these surveys is to be able to find areas to be set as

priority in the improvement work towards increasing employee satisfaction in a cost

efficient way.

A methodology well suited for this purpose is the use of Structural

Equation Models, which is also the case within Ennova (Williams et al., 2003). A

structural model has been defined as European Employee Index Model (EEI model),

which is shown in Figure 3.1. (Eskildsen & Dahlgaard, 2000; Eskildsen et al., 2004).

Within the framework of Ennova, Partial Least Squares (PLS) is applied as the common

statistical method. The usage of PLS in employee satisfaction measurements, as within

Ennova, is based on research and many authors have argued that PLS is showing several

advantages in comparison to the covariance-based methods (Chin, 1998; Fornell &

Bookstein, 1982). For more details of PLS from a theoretical perspective as well as

algorithms see, for example, Lohmöller (1989); Wold (1985); Fornell & Cha (1994);

Tenenhaus, et al., (2005) and Vilares, et al., (2005).

The aim within Ennova is to analyse the direct impact from seven

different antecedents for employee satisfaction and loyalty; Reputation, Senior

Management (SM), Immediate manager (IM), Daily work, Cooperation, Development

and Remuneration.

Figure 3.1. European Employee Index Model

Reputation

Senior Management

Immediate Superior

Co-operation

Daily Work

Remuneration

Development

Action areas Result areas

Perception Behaviour

Satisfaction

Motivation

Satisfaction &

MotivationLoyalty

Retention

Commitment

- 74 -

Ennova conducts an annual representative survey, European Employee Index (EEI), in a

number of countries over the world, with a stronger focus on the Nordic countries

specifically.

This study will use empirical data from EEI and by re-modelling the EEI

model be able to analyse the in-direct impact from these two leadership dimensions.

Through this it should be possible to evaluate how the leadership dimensions role in an

Employee Engagement model could, or maybe should, be settled. The empirical

analysis will cover 4 years of data in 15 European countries, 3 Asian countries, 3

countries in South America and USA in total 22 countries worldwide.

3.2 European Employee Index

In 2000 Markedskonsult A/S (changed name to Ennova in 2006) introduces the Danish

employee Index. The scope widened to constitute the Nordic countries in 2001, which

was evaluated in a joint project between Markedkonsult A/S and CFI group in 2004

(Eskildsen et al., 2004) and the project changed name to Nordic Employee Index. The

aim in that project was to develop and test a generic model of measuring employee

satisfaction and loyalty as well as their antecedents. The model developed, has been

based on wide academic research within this field (Baker, 1995; Eby et al., 1999, de

Jonge et al., 2001; Eskildsen & Dahlsgaard, 2000) and one of the main purposes was to

develop a model for measuring employee satisfaction regardless of organisational

settings.

In 2002 this Nordic project was incorporated on a European arena and by

that also a new label of the survey was at hand, namely European Employee Index. The

scope of the survey increased over the years to include over 20 countries from 2007.

The largest focus is still on Europe, but includes also USA, Japan, China, India and

Brazil among others, so by now it is more recognised as a global initiative.

- 75 -

In the EEI model there are seven different drivers, i.e. exogenous variables

where the aim is to analyse the relative impact each exogenous variable has on

employee satisfaction and loyalty. As mentioned earlier the exogenous variables are;

Reputation – questions covering the perception among employees on the

general knowledge about their organisation. Senior Manager (i.e. Senior management)

– questions within this area to cover the top management’s abilities. Immediate

manager – questions within this area to receive employees’ perception on perceived

abilities and qualifications on the manager to which they report to. Daily work – area of

questions to capture the perception on employees’ daily activities and working

conditions. Cooperation – block of questions with regards to perception of quality of

working with people in the organisation. Development – the perception from employees

on their individual increase of competency and Remuneration – general questions to

capture employees perception on compensation within their organisation in relation to

other work places.

3.3 Empirical Study Design

Analyses done earlier on the effects (direct effects) from the seven different drivers in

the EEI model have shown that generally the management perspectives do not have any

high direct effect on employee satisfaction. Should the leadership dimension not be

prioritised then? The discussion on this should be that working with leadership

development might not be a priority in order to raise satisfaction and loyalty directly but

leadership on different levels has influences on satisfaction among employees “through”

other dimensions, i.e. by having an effect on factors that can be shown to have a direct

effect.

The purpose of this study is to analyse the in-direct effect that SM and IM

have on employee satisfaction, i.e. analyse the effect from the two specified leadership

dimensions on the remaining five factors being considered as antecedents in the EEI

model. Figure 3.2, presents the re-arranged EEI model to fulfil this purpose.

- 76 -

Figure 3.2. Rearranged EEI model

Re-arranging the structural equation model and pursue the PLS analysis in a three-step-

model will show how large effect senior and immediate management have and by that

the influence management has when analysing on a broader range. Figure 3.2

constitutes a model with some similarities to the perception on effect scheme in the

EFQM excellence model (EFQM, 2011), where the concept is based on that

performance is driven through policy and strategy with the focus on customers, people

(employees) as well as society as base for business excellence, but with leadership as

the driver. This coincides with many organisational theories with regards to business

excellence, focusing on leadership from this perspective. (Shingo Prize, (2011),

Baldridge, (2009-2010)). Even the well-defined framework of the Balanced Scorecard,

with which organisations are able to study several performance measures,

simultaneously has the idea of leadership as the driver for business excellence (Kaplan

& Norton, 1996). This gives the theoretical perspective of accepting leadership’s role

from a business excellence perspective, but the idea of re-arranging a well-defined

model for Employee Engagement has not, according to the author, been conducted to

any higher extent.

- 77 -

The scenario presented, will add in knowledge as to the leadership

dimensions; i) placement in an Employee Engagement model and ii) the impact/effect

from leadership dimensions through factors included in the EEI model. From

organisational theory this scenario is evident, but from an empirical perspective there

are implications to be mentioned. The data used in this study can only discuss results

following the factors used in the EEI model; however the general driving factors on

employee satisfaction included in the EEI model are well founded from previous lines

of research. Further on, no evaluation towards the questions or data collection method

or any at such will be pursued.

Hypotheses surrounding the outcome of an analysis conducted as defined

above are as follows; i) SM have a larger effect through reputation compared to IM.

This due to the underlying responsibility of branding a company is more directed

towards SM than IM. This should be evident in a set-up presented here. Another

hypothesis is that; ii) IM has a large effect through, for instance, daily work. This due to

that IM should have a more significant impact on a more daily basis for the employees

in comparison with SM. An overall hypothesis is that senior management has a high

influence/effect through all five factors depending on the organisational hierarchy that is

at least assumed in a business. This should also be evident in a set-up as described in

this study.

The data used in this study originates from European Employee Index

survey, which is an annual survey conducted by Ennova since 2001. The number of

countries in total has increased over the years and in 2010 there were 22 countries

represented in the survey constituted by approximately 25.000 answers from employed

people between the ages of 18 and 70. The data has mainly been collected via web in all

countries in cooperation with a sub-contractor, but approximately 40% telephone

interviews (CATI) have been added in Denmark, Norway and Sweden2.

2 The data used in this study are collected mainly via web, with an extension of CATI in three Nordic

countries. The sub-supplier uses web panels that imply that it is not fully representative towards the

country’s population but representative towards the working part of the population having internet access.

Looking into the panel set-up show that this data has a focus towards the industrialised part of the

countries and therefore some implications when discussing the development countries are at hand.

- 78 -

A stronger focus will be directed towards the three Nordic countries in this

study. The largest shares of countries included in the European Employee Index survey

are European together with the extended focus on three of the Nordic countries. The

countries included here, are presented in Figure 3.3.

Figure 3.3. Countries included in this study

To be able to analyse if there are systematic similarities and/or differences the data will

be analysed using PLS following the SEM model in Figure 3.2 both country-wise and

global-wise. The general analysis will cover country data, from two perspectives:

A: PLS Analysis country-wise over 4 years (2007-2010).

B: PLS Analysis of continents3 in 5 parts of the world, over 4 years (2007-2010).

The next step will be to take into consideration i) background information and ii)

organisational information. The three perspectives chosen for this study are c) gender d)

age and e) if respondent is a manager or not. However, due to implications in data c)

through e) will only be analysed in three of the Nordic countries, i.e. Denmark, Sweden

and Norway and if any systematic differences can be seen, this will give input to further

research within this area, but cannot be generalised in a more wider perspective. The

steps of analysis will therefore cover:

C: PLS analysis of gender in the Nordic countries covering 4 years of data.

3 The continents being studied are: USA/North America, South America, Europe and Asia. Asia has been

divided into two parts; i) China & India and ii) Japan.

Brazil Chile Mexico Czech Republic Ireland Poland Italy United Kingdom

China India Japan Estonia Russia France Germany Netherlands

Denmark Sweden Norway Finland Spain USA

- 79 -

D: PLS analysis of age in the Nordic countries covering 4 years of data.

E: PLS analysis of manager vs. non-managers in the Nordic countries covering 4 years

of data.

The structural model including the parameters for the re-arranged EEI model is seen in

Figure 3.4. Noticeable is that the direct effects from the two leadership dimensions

towards the result parameter (Satisfaction & Motivation) are still included. Even though

the model in Figure 3.4 shows explicitly that there are only two exogenous variables,

the choice has been to keep the original indexation of the latents according to the EEI

model in Figure 3.1. This is only to ease the comparison.

Figure 3.4. Structural model for the re-arranged EEI model, including parameters and causal

connections

The structural equations for the latent variables shown in Figure 3.4, can be viewed in

equation (3.1) – (3.7).

2

3

1

4

5

6

7

1 2

12

42

52

62

72

13 43

53

63

73

11

14

15

16

17

12

13

Senior Management

ImmediateManager

Reputation

Co-operation

Daily Work

Remune-ration

Develop-ment

Satisfaction& Motivation

Loyalty21

- 80 -

(3.1)

(3.2)

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)

The analytical scheme described earlier will be evaluated based on , i.e. model fit,

The five factors being affected from the two leadership dimensions, i.e. , the size of

impact from i) senior management (SM) and ii) immediate manager (IM) as well as the

relative effect between the two leadership dimensions ( ) will be evaluated

further. The simple equation for relative effect is presented in (3.8).

- 81 -

, for each , i=1,4,5,6,7 ; j=1,4,5,6,7 (3.8)

In (3.8) the relative effect is based on senior management’s effect on each to be able

to calculate how large a percentage of the total effect that originates from the senior

management perspective relative immediate manager. There could of course be set the

other way around but a choice has been made to discuss the findings, throughout this

study, in terms of senior management relative immediate manager.

In a set-up as in Figure 3.2 it would also be interesting to determine the

relative importance between the two leadership dimensions analysed, meaning how

much is the contribution from each leadership dimension in for each of the five

factors respectively. Researchers focusing on this area have been debating over the

methods proposed ever since the first debate on the subject was published in the

beginning of the sixties (originated from Englehart, 1936), which also becomes evident

considering the large amount of articles concerning this area in the years to come

(Hoffman, 1960; Budescu, 1993; Darlington, 1968; Kruskal (1987); Kruskal & Majors,

1989; Pratt (1987); Thomas & Decady, 1999; Grömping (2007)). One possible approach

in calculating the relative importance in a structural equation is to consider the original

formula in a matrix, the coefficient of multiple determination, in (3.9)

(3.9)

Where y is the dependent variable and x is designating the independent variable. If only

one predictor, , i.e. a simple linear regression with one independent variable, (3.9)

reduces to the simple squared correlation as an estimation of . To be able to evaluate

the relative importance among the parameters, when more than one independent factor

is at hand, one need to consider the coefficient vector, , which in standardised form

could be written as

- 82 -

(3.10)

By substituting (3.9) with the Identity matrix, denoted by, , we obtain (3.11)

(3.11)

(3.11) is then find to be identical to (3.12) by adding in knowledge from (3.10) into

(3.11).

(3.12)

The parameters from the quadratic matrix formulation in (3.12) is then calculated as

∑ ∑

(3.13)

If , the right side in (3.13) can be re-written as follows

∑ ∑ ∑

(3.14)

The far right part in (3.14) is considered the multicollinearity contribution and if we

have low level of multicollinearity, will be low, which makes this part negligible.

We are then able to estimate relative importance by use of far left part in (3.14), which

- 83 -

are the standardised coefficients in a regression. This is one alternative of estimating

relative importance.

Another alternative in evaluating relative importance of independent

variables in a regression form is to consider an estimation of as in (3.15)

(3.15)

Which is calculated according to (3.16)

∑ (3.16)

(3.16) can be re-written as in (3.17), where ‘g’ is equal to the un-standardised regression

coefficient.

∑

(3.17)

The causal scheme set up of the structural equation model for this study implies that

is the same in all cases. The sum of

will estimate the total . This means that

(3.17) can be used to calculate each of the five factors’ relative importance and the sum

is the total . From (3.17) we see that the right part of the numerator is referred to the

standardised beta coefficient (b) in an ordinary regression, meaning that (3.17) could be

rewritten as in (3.18) for factor i.

(3.18)

- 84 -

To evaluate the relative importance for each leadership dimension towards each of the

five factors, we can apply (3.18). Earlier we studied the relative effect in between the

two leadership dimensions. The same idea will be applied here. After calculating the

relative importance per leadership dimensions for each factor, we then, by setting SM

( ) as the relative factor to study in comparison between the two leadership factors, we

calculate the overall relative importance between the leadership dimension in each of

the five factors according to (3.21).

(3.21)

Where i=1,4,5,6,7

(3.21) is used in this study to estimate the relative importance between the two

leadership dimensions for each of the five factors having a causal relation with the two

leadership dimensions (SM and IM). This follows theory proposed by Pratt (1987). One

could argue that it is not entirely straight-forward procedure, since in some cases, there

is a possibility of negative effects. However, this is not the case in this study,

considering the model in Figure 3.5. The model specification and the underlying theory

are based on an econometric approach where the possibility of accepting negative

effects in the causal scheme is equal to zero. This is an approach highly evident in many

economic theories. The estimation on relative importance following (3.18) will

therefore add an understanding of the relative importance in this study. As mentioned

before there are several proposed alternatives, but the author has chosen to follow Pratt

because of the conditions underlying this model.

3.4 Results

We will only present results for the three Nordic countries as an example. All other

results are to be found in appendix.

- 85 -

The results for the calculated relative effect and relative importance on

country level are viewed in Table 3.1 and Table 3.2 respectively.

Generally in all analysis done, a good model fit is evident ( ),

indicating that we are able to explain large amount of variation in this model set-up,

with some exceptions.

Table 3.1. Relative effects between SM and IM, where relative effects are calculated according to

It is evident from the results in Table 3.1 that Senior Management (SM) has a relatively

large effect compared to Immediate Manager (IM) on all factors; however a pattern is

quite distinctive implying the largest effect is shown towards Reputation and

Remuneration. This is not surprising results, considering the strategic organisational

focus, which is evident from a top management perspective. The effect between SM and

the three remaining factors are not as straight forward, however generally on a lower

level compared to Reputation and Remuneration, which indicate that there is a larger

effect originating from IM on these factors, on a relative basis. An interesting

Reputa

-tion

Coop-

eration

Daily

Work

Remune-

ration

Develop

-ment

Denmark 2007 74% 56% 60% 67% 54% 71%

2008 83% 57% 57% 73% 52% 72%

2009 90% 55% 61% 68% 53% 63%

2010 83% 65% 70% 81% 66% 61%

Norway 2007 86% 56% 64% 78% 60% 69%

2008 84% 52% 54% 75% 53% 70%

2009 91% 59% 64% 71% 55% 67%

2010 86% 58% 65% 82% 64% 67%

Sweden 2007 85% 64% 74% 80% 71% 70%

2008 86% 60% 60% 75% 61% 68%

2009 92% 67% 68% 74% 64% 68%

2010 91% 63% 73% 78% 66% 68%

CountryModel

fit R^2

Relative effect on each factor, based on SM!

Year

- 86 -

observation is the increasing effect from SM during the financial crisis (2008 and

onward), generally.

Overall, the results are implying that there are high effects between SM

and the five factors, which according to earlier stated hypothesis, would be evident. An

explaining factor would be the organisational, hierarchical settings in interpreting SM

relative IM. This is a pattern that is evident generally in the analyses conducted in this

study.

Table 3.2 Relative importance, based on SM, on each factor calculated according to

The relative importance per factor in Table 3.2 follows the same pattern as estimated

relative effect, showing a large contribution from SM on each factor, but most evident

for - again - Reputation and Remuneration. Relative effect and relative importance are

at the same level in comparison. An interesting finding is that it seems as though both

the relative effect and relative importance increase for SM, following the four years of

data being studied, which could be explained by the global financial crisis, where it

could be natural to find that the dependence on SM is stronger. This trend is however

Reputation Cooperation

Daily

Work Remuneration Development

Denmark 2007 78% 57% 62% 70% 54%

2008 87% 57% 57% 77% 52%

2009 93% 56% 63% 71% 53%

2010 86% 67% 72% 84% 68%

Norway 2007 88% 55% 64% 80% 60%

2008 86% 50% 52% 77% 51%

2009 93% 58% 65% 73% 54%

2010 88% 58% 65% 85% 65%

Sweden 2007 89% 65% 77% 83% 74%

2008 89% 60% 60% 78% 61%

2009 94% 68% 69% 77% 65%

2010 93% 64% 75% 81% 67%

Country

Relative importance on each factor, based on SM!Year

- 87 -

not as evident in countries like Norway and Sweden, which are examples of countries

not as affected by the financial crisis, as in for instance Denmark, where a much larger

effect from SM is seen.

Presenting a more graphic view of the results on relative effects, an example is included

in Figure 3.5. The results here are based on the BRIC countries (Brazil, Russia, India

and China). It can be seen that the relative effect are quite substantial for SM generally.

Figure 3.5. Relative effects between SM and IM, where relative effects are calculated according to

, BRIC countries

Results prepared according to a more organisational perspective are presented in Table

3.3. These results show the similarities and differences depending on if the respondent

is i) a manager or ii) non-manager (denoted ‘employee’ in following discussion). Due to

implications of not having knowledge on whether a respondent is a manager or not in all

countries except the Nordic countries; this analysis has only been prepared for the three

of the Nordic countries included in this study.

- 88 -

Table 3.3. Relative effects and Relative Importance between SM and IM, where relative effects are

calculated according to

and relative importance according to

,

manager vs employee

Results in Table 3.3 follow the same discussion as earlier, implying that the effect from

SM is larger in relation to IM. The results are further showing that effect from SM,

generally, is higher from the manager’s perspective compared to the employees. These

results imply that managers tend to rely on a higher extent more on the senior

managements responsibility on the factors investigated. It is not a straight-forward

pattern and should be looked into more.

Table 3.4 and 3.5a,b presents results based on a socio-demographic

grouping of data.

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

2007 Manager 78% 80% 76% 51% 59% 81% 83% 80% 51% 60% 71%

Employee 73% 54% 58% 69% 53% 77% 54% 59% 72% 54% 71%

2008 Manager 87% 60% 66% 72% 63% 91% 62% 69% 76% 67% 72%

Employee 82% 56% 55% 74% 50% 86% 56% 55% 78% 49% 72%

2009 Manager 91% 63% 82% 69% 64% 94% 66% 86% 73% 67% 62%

Employee 90% 54% 59% 67% 51% 93% 54% 60% 70% 50% 63%

2010 Manager 93% 59% 43% 75% 63% 95% 61% 41% 79% 66% 58%

Employee 81% 67% 75% 82% 67% 84% 69% 78% 85% 69% 61%

2007 Manager 82% 78% 63% 71% 52% 84% 81% 64% 72% 52% 72%

Employee 86% 51% 63% 79% 61% 89% 49% 64% 82% 61% 67%

2008 Manager 85% 57% 56% 64% 57% 88% 55% 55% 64% 57% 72%

Employee 84% 52% 54% 77% 52% 86% 49% 51% 80% 49% 69%

2009 Manager 88% 60% 71% 58% 52% 90% 59% 72% 57% 50% 65%

Employee 91% 59% 62% 74% 55% 93% 58% 62% 76% 54% 67%

2010 Manager 90% 66% 80% 77% 77% 92% 67% 82% 79% 79% 67%

Employee 86% 58% 63% 84% 62% 88% 58% 63% 87% 63% 67%

2007 Manager 87% 73% 73% 79% 72% 91% 77% 76% 83% 75% 70%

Employee 85% 62% 73% 79% 70% 88% 62% 76% 83% 72% 69%

2008 Manager 92% 60% 62% 63% 58% 94% 61% 63% 64% 58% 71%

Employee 85% 60% 59% 77% 61% 88% 60% 58% 81% 61% 67%

2009 Manager 100% 81% 70% 71% 59% 100% 84% 73% 75% 61% 64%

Employee 91% 65% 67% 75% 65% 93% 66% 68% 77% 65% 67%

2010 Manager 96% 55% 91% 66% 76% 97% 55% 94% 65% 78% 67%

Employee 90% 66% 70% 80% 64% 92% 67% 71% 83% 65% 67%

Country YearEmployment

type

Relative effect on each factor, based on SM!Denmark

Norway

Sweden

Relative Importance on each factor, based on SM!Model fit

R^2

- 89 -

Table 3.4. Relative effects and Relative Importance between SM and IM, where relative effects are

calculated according to

and relative importance according to

, gender

Still the same discussion with regards to highest relative effect and importance

depending on SM or IM follows here. Distinction between the gender seems most

evident in that relative effect from a male perspective is quite status quo over the years,

while the effect increases in favour of SM especially on Daily work and Remuneration

from a female perspective, this is highly evident in Denmark, which was also the

country that was most affected by the financial crisis out of the three countries presented.

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

2007 Male 80% 63% 55% 59% 54% 83% 66% 55% 61% 54%

Female 70% 50% 65% 73% 54% 73% 49% 67% 77% 54%

2008 Male 89% 71% 65% 75% 61% 88% 47% 62% 82% 61%

Female 76% 44% 48% 72% 43% 89% 62% 67% 78% 58%

2009 Male 88% 49% 58% 67% 48% 91% 76% 73% 83% 78%

Female 92% 64% 66% 68% 59% 87% 54% 80% 84% 69%

2010 Male 83% 64% 60% 74% 62% 92% 75% 67% 79% 63%

Female 83% 68% 80% 89% 71% 80% 41% 46% 76% 40%

2007 Male 85% 49% 61% 78% 60% 86% 48% 52% 67% 61%

Female 86% 62% 66% 76% 59% 87% 51% 52% 84% 42%

2008 Male 84% 50% 54% 66% 62% 84% 60% 59% 76% 60%

Female 84% 53% 54% 81% 47% 92% 60% 61% 79% 62%

2009 Male 86% 53% 60% 68% 54% 91% 47% 58% 70% 47%

Female 97% 65% 68% 74% 56% 94% 67% 69% 72% 61%

2010 Male 80% 60% 62% 75% 57% 88% 52% 61% 70% 53%

Female 91% 56% 68% 89% 72% 97% 66% 69% 76% 56%

2007 Male 87% 72% 70% 79% 74% 92% 69% 70% 76% 60%

Female 84% 56% 77% 81% 68% 96% 67% 68% 78% 70%

2008 Male 81% 59% 59% 73% 60% 87% 67% 62% 78% 65%

Female 89% 61% 62% 76% 61% 85% 69% 82% 91% 73%

2009 Male 90% 68% 68% 73% 60% 83% 61% 62% 78% 57%

Female 95% 66% 66% 75% 68% 93% 54% 68% 92% 73%

2010 Male 88% 52% 68% 78% 65% 90% 51% 69% 81% 66%

Female 94% 76% 78% 76% 66% 95% 79% 81% 79% 67%

Den

mar

kN

orw

ay

Swe

den

Relative Importance on each factor, based on SM!Country Year Gender

Relative effect on each factor, based on SM!

- 90 -

Table 3.5a. Relative effects and Relative Importance between SM and IM, where relative effects are

calculated according to

and relative importance according to

, age categorised – Denmark and Norway.

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

Age: 18-29 years 74% 66% 61% 66% 55% 79% 71% 65% 71% 58% 69%

Age: 30-39 years 80% 52% 65% 63% 55% 85% 52% 69% 66% 57% 72%

Age: 40-49 years 67% 69% 59% 67% 64% 69% 71% 59% 70% 65% 69%

Age: 50-59 years 69% 37% 51% 66% 39% 70% 32% 49% 67% 34% 73%

Age: 60 years or older 90% 48% 48% 71% 62% 92% 48% 44% 75% 63% 73%

Age: 18-29 years 86% 57% 43% 66% 51% 90% 58% 39% 69% 50% 78%

Age: 30-39 years 88% 51% 60% 71% 51% 91% 50% 61% 74% 50% 71%

Age: 40-49 years 89% 69% 64% 76% 45% 92% 71% 65% 78% 41% 70%

Age: 50-59 years 69% 57% 60% 75% 66% 72% 58% 61% 79% 69% 70%

Age: 60 years or older 81% 11% 39% 77% 49% 84% 8% 36% 79% 47% 71%

Age: 18-29 years 84% 55% 73% 69% 47% 87% 59% 79% 73% 47% 66%

Age: 30-39 years 82% 61% 54% 61% 48% 85% 63% 54% 63% 47% 66%

Age: 40-49 years 88% 49% 59% 68% 52% 91% 47% 61% 71% 52% 68%

Age: 50-59 years 100% 48% 58% 63% 56% 100% 47% 60% 65% 57% 52%

Age: 60 years or older 92% 83% 62% 79% 64% 94% 85% 64% 83% 66% 66%

Age: 18-29 years 85% 45% 63% 65% 62% 88% 42% 62% 65% 61% 61%

Age: 30-39 years 88% 75% 75% 95% 69% 91% 77% 78% 96% 71% 59%

Age: 40-49 years 81% 72% 61% 76% 59% 85% 76% 62% 80% 61% 66%

Age: 50-59 years 78% 59% 75% 78% 70% 82% 59% 78% 81% 73% 57%

Age: 60 years or older 83% 60% 65% 77% 71% 87% 62% 66% 80% 74% 63%

Age: 18-29 years 75% 69% 69% 69% 65% 79% 71% 72% 72% 68% 71%

Age: 30-39 years 88% 53% 60% 82% 61% 90% 52% 60% 85% 61% 70%

Age: 40-49 years 99% 49% 55% 66% 55% 99% 47% 54% 67% 54% 70%

Age: 50-59 years 74% 51% 62% 79% 61% 76% 48% 61% 83% 61% 69%

Age: 60 years or older 96% 78% 86% 79% 57% 96% 79% 86% 83% 55% 63%

Age: 18-29 years 74% 51% 50% 74% 44% 78% 50% 48% 79% 42% 69%

Age: 30-39 years 82% 55% 49% 69% 55% 85% 53% 45% 71% 52% 74%

Age: 40-49 years 91% 50% 54% 72% 62% 93% 46% 51% 74% 61% 68%

Age: 50-59 years 85% 60% 55% 69% 53% 87% 59% 52% 69% 50% 70%

Age: 60 years or older 87% 33% 52% 73% 61% 88% 26% 48% 73% 59% 62%

Age: 18-29 years 81% 68% 70% 77% 78% 85% 69% 70% 80% 81% 64%

Age: 30-39 years 92% 47% 54% 68% 48% 94% 46% 54% 70% 47% 72%

Age: 40-49 years 92% 60% 67% 63% 55% 93% 58% 67% 63% 53% 68%

Age: 50-59 years 88% 61% 64% 72% 54% 90% 60% 65% 73% 52% 65%

Age: 60 years or older 100% 69% 67% 84% 66% 100% 72% 69% 88% 68% 65%

Age: 18-29 years 81% 64% 76% 82% 66% 84% 66% 80% 85% 68% 67%

Age: 30-39 years 87% 47% 54% 88% 60% 90% 43% 51% 91% 59% 73%

Age: 40-49 years 82% 69% 68% 76% 71% 84% 71% 68% 78% 73% 64%

Age: 50-59 years 84% 52% 58% 73% 62% 88% 51% 58% 76% 63% 69%

Age: 60 years or older 97% 68% 72% 80% 70% 97% 69% 71% 82% 71% 57%

2009

Age interval

Relative effect on each factor, based on SM!

2007

2008

Relative Importance on each factor, based on SM!Model fit

R^2

2009

2010

2007

De

nm

ark

No

rway

2008

2010

Country Year

- 91 -

Table 3.5b. Relative effects and Relative Importance between SM and IM, where relative effects are

calculated according to

and relative importance according to

, age categorised – Sweden.

The results on relative effects divided by age intervals as shown in Table 3.5a and 3.5b

follow the discussion of large effect related to SM. However, there seem to be some age

differences evident. Employees in their fifties and above are showing larger effects in

favour of Senior Management overall, while a slight opposite picture is shown for

employees in younger age categories. The pattern is scattered out from the age

perspective as has been the case in earlier presented results, so this should be analysed

further. The relative importance presented shows a large effect from senior management

overall, as is the case in all results presented.

The socio demographic, i.e. gender and age, differences, which appear to

be present in the relative effects presented earlier, is interesting to analyse more in depth

to be able to conclude if there are significant differences. Gender and age differences

have been areas of research for many years in several different contexts and

perspectives; psychologically, behaviourally, environmentally as well as research on job

satisfaction to mention a few areas (see for instance Deaux & Major, 1987) and there

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

Age: 18-29 years 89% 55% 76% 80% 67% 93% 56% 81% 84% 71% 72%

Age: 30-39 years 83% 69% 70% 76% 74% 85% 71% 71% 80% 76% 71%

Age: 40-49 years 91% 62% 73% 70% 71% 93% 62% 76% 72% 73% 70%

Age: 50-59 years 85% 62% 79% 85% 73% 89% 64% 83% 89% 77% 69%

Age: 60 years or older 67% 74% 49% 100% 62% 69% 78% 47% 100% 64% 69%

Age: 18-29 years 84% 55% 54% 73% 66% 88% 56% 52% 75% 70% 69%

Age: 30-39 years 92% 55% 53% 72% 59% 95% 55% 53% 76% 60% 69%

Age: 40-49 years 73% 55% 65% 68% 57% 75% 54% 65% 70% 56% 70%

Age: 50-59 years 83% 62% 40% 75% 58% 85% 63% 35% 78% 57% 64%

Age: 60 years or older 100% 92% 86% 86% 70% 100% 95% 88% 90% 71% 71%

Age: 18-29 years 100% 62% 69% 61% 66% 100% 63% 70% 61% 68% 68%

Age: 30-39 years 87% 66% 59% 72% 63% 90% 67% 59% 75% 64% 65%

Age: 40-49 years 84% 58% 69% 71% 64% 87% 58% 72% 75% 66% 70%

Age: 50-59 years 100% 76% 62% 73% 60% 100% 78% 61% 75% 59% 65%

Age: 60 years or older 100% 68% 80% 74% 60% 100% 69% 81% 75% 60% 70%

Age: 18-29 years 79% 55% 61% 75% 61% 82% 53% 61% 81% 63% 68%

Age: 30-39 years 98% 61% 76% 78% 67% 99% 61% 79% 82% 69% 67%

Age: 40-49 years 86% 74% 81% 82% 68% 88% 76% 83% 85% 69% 69%

Age: 50-59 years 90% 53% 54% 49% 60% 91% 52% 53% 48% 60% 67%

Age: 60 years or older 100% 68% 73% 90% 70% 100% 69% 74% 89% 71% 68%

Model fit

R^2

2007

2008

2009

2010

Swe

den

Country Year Age intervalRelative effect on each factor, based on SM! Relative Importance on each factor, based on SM!

- 92 -

are evidence pointing towards differences in gender and age, for instance in job

satisfaction research (Clark et al., 1996; Wharton et al., 2000; Eskildsen et al., 2003).

However, there are some scattered patterns regarding these differences (Chileshe &

Haupt, 2009; Eskildsen, et al., 2003), but due to former findings it is relevant to analyse

the data in order to see if we can state any significant difference in analysing impacts,

i.e. effects, in an employee engagement context in the three Nordic countries.

Hypotheses from a demographic perspective could be:

Hypothesis 3.1a: There exists a significant difference in relative effects on the five

factors between genders in the three Nordic countries.

Hypothesis 3.1b: There exists a significant difference in relative effects between

genders, over time, in the three Nordic countries.

Hypothesis 3.2a: There exists a significant difference in relative effects on the five

factors between the age groups defined.

Hypothesis 3.2b: There exists a significant difference in relative effects on the five

factors within the age groups defined, over time.

Numerous of research within the area of leadership and organisational theory focusing

on different perspective of outcome, i.e. performance, is evident and one perspective to

be mentioned is “leadership type”, (Jordan, P.J & Troth, A. 2011).

When splitting the respondents into managers and non-managers (i.e.

employees) the results above indicate a difference in impact structure, but also

considering the scattered pattern in relation to this. The question is, is there a difference

in impact structure depending on if you are a manager or not? One underlying reason

for looking into this could be to discuss the importance of social identification (van

Dick & Schuh, 2010). The meaning of social identification is to what extent a person

will perceive the union of i) themselves ii) the group overall and iii) the value of the

- 93 -

group membership (Tajfel, 1981). One could assume that out from the perspective

studied here there should either be a higher social identification from a manager point of

view in relation to employees or that they should be at the same level. If higher social

identification, we could assume also a higher impact towards Senior Management

following the definition of a stronger group identity, since individuals identifying

themselves with a group would also identify and internalise the values and norms of a

group. In this context the group would be defined by an organisation (van Dick, 2004,

Riketta, 2005; Riketta & van Dick, 2005). By this follows the intensity of striving to a

higher status within the group, which is an effect from social identification, which to

some extent could be more evident if a person is being a manager compared to

employees.

Even though we are not focusing on analyzing the social identification or

type of leadership, earlier research findings showing differences and effect out from

leadership imply that further analysis should be undertaken to see if we can find

evidence in the context studied here, supporting the following hypotheses;

Hypothesis 3.3a: There exists a significant difference in relative effects on the five

factors between managers and employees in the three Nordic countries.

Hypothesis 3.3b: There exists a significant difference in relative effects on the five

factors between managers and employees in the three Nordic countries, over time.

In order to undergo statistical tests in analysing the above stated hypotheses, 3.1a

through 3.3b, the author has chosen two separate tests to convey. One is a test between

the actual point of estimation for, say x1 in comparison with x2, indexing of Males and

Females in hypothesis 3.1a, for instance. The same idea is underlying all hypotheses

and so, the same process is undertaken. If we assume the samples in all hypotheses are

independent and following a normal distribution with mean zero, we can apply a two-

sided large sample t-test since in all cases, the sample is larger than 30 (n > 30).

- 94 -

We are here interested to analyse if there are significant differences in

relative effects which leads to the following null hypothesis:

(3.22)

The test statistic used in a large sample t-test is presented in (3.23)

(

)

√ (

)

(

)

(3.23)

It can be shown that the variance calculations of a quota could be calculated as in (3.24);

(

)

(

) (3.24)

The calculations in (3.24), which are based on effect estimates and the coefficient

variance (the variance of the estimated effects) are substituted in (3.23). The rejection

area when is;

(3.24)

Results for the three hypotheses testing on mean, following a test as in (3.23) are as

follows;

- 95 -

Hypothesis 3.1a: Test between gender

Table 3.6: Results from significance test of difference between males and females ( ), following a

Large sample test.

A star (*) indicates a significant difference, i.e. cases where we can reject the null

hypothesis. A straight line (-) indicate that we cannot calculate a test statistic, due to

effect being in-significant in the PLS analysis and therefore not being relevant.

There seem not to be a clear pattern of significant difference between the

genders being present. In Denmark the results are showing to a higher extent that there

are significant differences between males and females, which were also indicated earlier

(see Table 3.4). In the other two countries we cannot find evidence of a difference in

relative effects between the genders.

Hypothesis 3.2a: Test between age-groups

Reputation Cooperation Daily Work Remuneration Development

Denmark 2007 2.60* 3.36* -2.26* -3.24* -0.12

2008 3.69* 7.33* 3.81* 0.82 3.20*

2009 -0.94 -3.32* -2.03* -0.34 -1.73

2010 0.09 -1.16 -4.93* -4.40* -1.82

Norway 2007 -0.43 -3.27* -1.21 0.78 0.42

2008 0.01 -0.59 0.13 -4.24* 2.96*

2009 -3.30 -2.79* -1.94* -1.62 -0.40

2010 -3.27* 1.28 -1.55 -5.01 -3.05

Sweden 2007 0.71 5.01* -2.14* -0.65 1.45

2008 -2.22* -0.37 -0.69 -1.04 -0.34

2009 - 0.52 0.54 -0.65 -1.50

2010 -1.56 -5.56* -2.69* 0.71 -0.19

Test of difference between male and female

- 96 -

Table 3.7: Results from significance test of difference between age-groups within each country

( ), following a Large sample test.

Reputation Cooperation Daily Work Remuneration Development

2007 Age: 18-29 years -1.32 3.24* -0.85 0.67 -0.06

Age: 30-39 years 2.77* -4.17* 1.32 -1.01 -1.43

Age: 40-49 years -0.22 5.70* 1.56 0.19 3.30*

Age: 50-59 years -3.50* -1.35 0.30 -0.76 -2.47*

Age: 60 years or older

2008 Age: 18-29 years -0.44 1.01 -2.58* -1.13 0.02

Age: 30-39 years -0.15 -4.19* -0.87 -1.22 0.76

Age: 40-49 years 4.58* 2.78* 0.93 0.16 -3.11*

Age: 50-59 years -1.80 1.72 2.15* -0.28 1.79

Age: 60 years or older

2009 Age: 18-29 years 0.31 -1.06 3.25* 1.27 -0.11

Age: 30-39 years -1.67 2.63* -1.18 -1.71 -0.67

Age: 40-49 years - 0.10 0.20 1.12 -0.59

Age: 50-59 years - -6.40* -0.61 -3.19* -1.01

Age: 60 years or older

2010 Age: 18-29 years -0.54 -3.21* -1.82 -4.54* -0.88

Age: 30-39 years 2.00* 0.82 3.73* 6.42* 1.82

Age: 40-49 years 0.78 3.96* -4.14* -0.65 -2.15*

Age: 50-59 years -1.01 -0.29 2.32* 0.32 -0.22

Age: 60 years or older

2007 Age: 18-29 years -3.31* 3.46* 1.91 -3.14* 0.67

Age: 30-39 years -3.30* 0.75 1.09 4.72* 1.10

Age: 40-49 years 6.64* -0.33 -1.44 -3.69* -1.04

Age: 50-59 years -4.06* -4.77* -4.21* -0.01 0.44

Age: 60 years or older

2008 Age: 18-29 years -1.81 -0.81 0.04 1.04 -1.39

Age: 30-39 years -2.30* 0.96 -0.78 -0.57 -1.18

Age: 40-49 years 1.42 -1.98* -0.25 0.56 1.38

Age: 50-59 years -0.30 2.55* 0.46 -0.56 -0.87

Age: 60 years or older

2009 Age: 18-29 years -2.04* 3.30* 2.47* 1.85 4.34*

Age: 30-39 years 0.17 -2.40* -2.66* 1.02 -0.96

Age: 40-49 years 1.16 -0.18 0.67 -2.17* 0.16

Age: 50-59 years -2.75* -1.58 -0.57 -2.92* -1.64

Age: 60 years or older

2010 Age: 18-29 years -1.37 3.01* 4.16* -1.54 0.90

Age: 30-39 years 1.44 -4.81* -3.14* 4.07* -2.24*

Age: 40-49 years -0.64 4.30* 2.49* 0.85 1.99*

Age: 50-59 years -3.11* -3.15* -2.83* -1.62 -1.26

Age: 60 years or older

2007 Age: 18-29 years 1.48 -2.66* 1.41 0.89 -0.99

Age: 30-39 years -2.36* 1.93 -0.74 1.58 0.52

Age: 40-49 years 1.54 -0.09 -1.74 -4.09* -0.39

Age: 50-59 years 3.12* -2.57* 5.32* - 1.81

Age: 60 years or older

2008 Age: 18-29 years -1.53 0.06 0.01 0.20 1.03

Age: 30-39 years 4.65* -0.03 -2.33* 0.80 0.43

Age: 40-49 years -2.31* -1.62 4.62* -1.72 -0.21

Age: 50-59 years - -6.66* -8.00* -2.44* -1.79

Age: 60 years or older

2009 Age: 18-29 years - -0.75 1.46 -1.78 0.34

Age: 30-39 years 0.72 2.11* -2.37* 0.23 -0.17

Age: 40-49 years - -4.83* 1.69 -0.37 0.82

Age: 50-59 years - 1.82 -3.96* -0.14 -0.07

Age: 60 years or older

2010 Age: 18-29 years -3.63* -1.00 -2.62* -0.76 -0.82

Age: 30-39 years 3.51* -3.62* -1.47 -1.08 -0.24

Age: 40-49 years -1.08 5.18* 6.43* 7.87* 1.54

Age: 50-59 years - -2.94* -3.67* -9.05* -1.70

Age: 60 years or older

De

nm

ark

No

rway

Swe

de

nTest of difference between age-groups

- 97 -

The analysis has been conducted as a test between two neighbouring age-groups, i.e.

age classes, starting with the youngest age-group, for instance a test between “Age: 18-

29” and “Age: 30-39”.

From the results it is evident that we can find some cases where significant

differences in relative effect between neighbouring age classes are present. This is most

evident for Reputation, Cooperation and Daily Work, but the results are not clear-cut.

The significant differences seem to becoming even more evident, when viewing the

results for 2010, which is evident in all countries.

Hypothesis 3.3a: Test between manager and non-manager (i.e. employee)

Table 3.8: Results from significance test of difference between managers vs. employees ( ),

following a Large sample test.

Earlier studies have shown that there are differences between being a manager or an

employee from other perspectives, for instance in job satisfaction (Eskildsen et al.,

2003); however, out from the relative impact structure focusing on leadership, we are

not able to confirm a clear pattern of difference. We are able to find some significant

cases, but the results are too scattered to be able to conclude to a higher extent any

difference between being a manager or an employee. An interesting observation is that

Reputation Cooperation Daily Work Remuneration Development

Denmark 2007 1.22 8.44* 4.91* -3.64* 1.05

2008 1.43 1.00 2.43* -0.63 2.49*

2009 0.31 2.10* 7.07* 0.35 2.57*

2010 3.69* -2.08* -6.12* -2.07* -0.78

Norway 2007 -1.45 8.83* -0.12 -2.79* -1.72

2008 0.39 1.20 0.52 -3.94* 1.11

2009 -1.03 0.26 2.46* -3.91* -0.51

2010 1.49 2.39* 5.55* -2.32* 3.89*

Sweden 2007 0.76 3.94* 0.11 -0.05 0.47

2008 2.00* -0.06 0.73 -3.86* -0.54

2009 - 5.61* 0.64 -1.12 -1.15

2010 1.83 -2.55* 7.79* -3.99* 2.79*

Test of difference between manager and employee)

- 98 -

the results imply, to the highest extent, a significant difference being present in

Denmark.

We have been able to state both indications of differences over the years studied

together with significant differences in some specific cases. The indications towards a

time difference should be further investigated, meaning more in-depth analyses in

hypotheses 3.1b, 3.2b and 3.3b.

For simplicity we take gender as an example and follow the same

discussion with regards to age-groups and organisational categories (manager/not

manager). If we assume each calculated relative effect for each group/subject of gender

(male and female) as being independent and each year as the “treatments”, i.e. viewing

the relative effect as the response per year per subject we could then study the time

effect between the groups in a profile analysis. In profile analysis you are interested to

conduct the following three tests with regards to the profiles means over the treatments:

Test 3.1: Are the profiles parallel?

Test 3.2: Assuming the profiles are parallel, are the profiles coincident?

Test 3.3: Assuming the profiles are coincident, are the profiles level, i.e. are all the

means equal to same constant?

The different profiles interesting to be compared and analysed over time are i) the

gender comparison ii) age-group comparison and iii) the comparison between the

profile for manager vs. non-manager (employee).

Continuing the discussion from the gender perspective, as an illustration,

we show the mean vector (relative effects) for Reputation per gender in Figure 3.7 over

four years of time, taking Denmark as an example. However, the same procedure holds

for the other data considerations.

- 99 -

Figure 3.7. Relative effects, Reputation, for males and females in Denmark over four years’ time

(2007-2010).

If we specify the following vectors of means (i.e. relative effects) for each country:

[ ] (3.26)

[ ] (3.27)

We can then test the following hypothesis equivalent to the tests mentioned earlier;

Test 3.1 (parallel):

Test 3.2 (coincident):

Test 3.3 (level):

Where t=2007,2008,2009,2010

- 100 -

The null hypothesis for Test 3.1 (parallel profiles) could be re-written as in (3.28) using

a contrast matrix C (see (3.29))

(3.28)

[

] (3.29)

It can be shown that the rejection of at is when;

[(

)

]

(3.30)

Where and are calculated as in (3.31) and (3.32) respectively;

(3.31)

(3.32)

Where, p=4 (four specified point estimate over four years’ time). If profiles are parallel

it is equivalent to one mean being above the other one or vice versa. For further reading,

the author refers to Johnson & Wichern (1992).

- 101 -

Assuming that profiles are parallel, we should continue testing for profiles

being coincident. This implies that the sample for each profile is coming from the same

normal population. The specifications for the test statistic, , to conduct Test 3.2

(coincident profiles) are as follows.

(

√(

)

)

(3.33)

We reject the null hypothesis, coincident profiles, if

(3.34)

If the profiles are coincident, we continue further on to test if profiles are at level. This

means testing if all the means are equal to same constant. The test statistic for this in

(3.35)

[

]

(3.35)

We reject the null hypothesis, profiles at level, if

(3.36)

- 102 -

We are conducting the profile analysis based on very large samples; the consequence is

that at confidence level of 0.05, is approximately the same for all factors in all

countries when testing between gender, age and manager vs. employees. Due to the fact

that the sample per group is not of exact same size, we are using an average of the

sample sizes over the four time periods. This will not affect the profile testing, since the

differences are small together with the fact that we have very large sample sizes.

Denmark is taken as an example in the results presented below.

Applying Test 3.1, Test 3.2 and Test 3.3 specified earlier (denoted Test 1, Test 2 and

Test 3 in the following tables), according to the calculations above on the three

hypotheses, 3.1b, 3.2b and 3.3b, the following estimated test statistic for the three tests

in profile analysis are shown for Denmark and other results are to be found in appendix:

Table 3.9 presents the estimated test statistic ( ) in the three perspectives of profile

analysis of gender (Test 3.1), for the Danish data 2007-2010. A star (*) indicates a

significant differences, i.e. a rejection of the null hypothesis.

Table 3.9. Estimated , profile testing of males vs. females in Denmark over four years’ time.

The results reveal that we can reject hypothesis of the trend for male vs.

female being parallel, meaning that the development in relative effects does not follow

the same pattern over time for both gender. This is the same as for Norway, but not for

Parallel Coincident Level

Test 1 - T2 Test2 - T2 Test3 - T2

Reputation 13.04* 7.00 28.34*

Cooperation 51.9* 5.84 101.57*

Daily Work 34.08* 6.71 19.59*

Remuneration 20.41* 14.39* 88.59*

Development 13.14* 0.05 28.58*

De

nm

ark

- 103 -

Sweden. In Sweden the impact structures for male and female are parallel, meaning we

cannot find a significant difference between genders in Sweden.

Considering test 3.2, the result shows that the profiles are coincident for

all factors in all three countries. The interpretation of this is that the responses appear to

be the same. No test reveals any profiles being at level.

Viewing the results for age in Table 3.10, the same pattern is shown

generally. Minor parallelism when testing the older age-groups is seen, focusing on

Remuneration. Regarding Development, however, here we find parallelism in the

younger age intervals. Nearly all profiles are coincident, but only a few turns out to be

at level. The same discussion is followed in the Norwegian and Swedish results (see

appendix).

Table 3.10. Estimated , profile testing age groups in Denmark over four years’ time.

Parallel Coincident Level

Test 1 - T2 Test2 - T2 Test3 - T2

Reputation 18 - 29 30 - 39 1.33 0.99 20.19*

30 - 39 40 - 49 12.44* 2.80 15.97*

40 - 49 50 - 59 83.95* 1.76 83.78*

50 - 59 60 - 34.33* 8.01* 319.8*

Cooperation 18 - 29 30 - 39 34.21* 2.10 32.32*

30 - 39 40 - 49 37.86* 6.44 113.4*

40 - 49 50 - 59 18.99* 40.35* 57.89*

50 - 59 60 - 28.60* 0.00 24.43*

Daily Work 18 - 29 30 - 39 21.68* 1.36 52.18*

30 - 39 40 - 49 13.74* 1.29 49.93*

40 - 49 50 - 59 17.02* 0.01 2.92

50 - 59 60 - 7.05 5.00 45.96*

Remuneration 18 - 29 30 - 39 38.50* 5.77 1.34

30 - 39 40 - 49 39.07* 0.14 236.4*

40 - 49 50 - 59 1.57 0.29 17.45*

50 - 59 60 - 5.82 3.78 26.03*

Development 18 - 29 30 - 39 0.76 0.31 9.76*

30 - 39 40 - 49 6.16 0.03 29.84*

40 - 49 50 - 59 25.47* 0.64 19.48*

50 - 59 60 - 10.11* 0.78 33.68*

De

nm

ark

Age groups tested

- 104 -

The third hypothesis concerns the profiles of managers vs. non-managers, i.e.

employees. A presentation of the results from the profile analysis is to be found in Table

3.11.

Table 3.11. Estimated , profile testing managers vs. employees in Denmark over four years’ time.

From the profile testing it is quite obvious that we find significant differences between

managers and employees with regards to the calculated relative effects over time. The

same pattern is revealed in the other two countries as well.

The test above shows that we to a large extent, not all cases, give a confirmation to the

hypothesis 3.1b, 3.2b and 3.3c, where we stated a hypothesis of having difference over a

four years’ time period.

Parallel Coincident Level

Test 1 - T2 Test2 - T2 Test3 - T2

Reputation 4.93 9.425* 60.95*

Cooperation 38.56* 14.59* 127.89*

Daily Work 117.88* 4.88 385.06*

Remuneration 13.28* 11.85* 173.58*

Development 6.68 6.07 3.13

De

nm

ark

- 105 -

3.5 Conclusion and Discussion

The aim of this study was to analyse the in-direct effects from two management

perspectives in an employee engagement model. To fulfil this purpose a re-arrangement

of the European Employee Index model (EEI model) was done, by placing i) Senior

Management (SM) and ii) Immediate Manager (IM) far left in the model. The effect

from these two management perspectives towards the five factors also present in the

EEI model has been the overall target of attention to analyse.

The main focus was to analyse the above from a i) country perspective ii)

organisational perspective and ii) socio-demographic perspective in 22 countries in total.

PLS has been the statistical method chosen.

The results presented show that SM are found to be highly affecting

reputation and remuneration on a general basis out from the data analysed. Even though

we are also able to find that cooperation, daily work and development are to a higher

extent also being affected by immediate manager, overall we find that SM in most of

the cases outperform relative to IM. We are also able to see that there seems to be an

increasing effect from SM following a timeline; a reason for this might be due to the

financial crisis being present on a global basis during the latter part of the time periods

studied. Further analysis on this has not been undertaken here.

Immediately it appears to be some differences showing up in the relative

effects when studying i) male vs. female ii) age-groups and iii) managers vs. employees.

A test of differences between the specified target groups reveals that only some cases

are showing significant differences, where this is most evident in Denmark, meaning

that socio-demographic and organisational differences are evident in especially

Denmark to a larger extent. The results here partly confirm earlier studies on these

characteristics, being studied from other perspectives (Eskildsen et al., 2003). A profile

analysis has been conducted, in order to analyse if there are some trend effects

following a time line of four years. The findings in the profile analysis is that we to a

high extent do find differences between the characteristics studied; however, the pattern

is not straight-forward. For instance, studying the test for gender in Sweden, this is an

- 106 -

example where we find the gender profiles to be parallel. This is the only country

showing such strong evidence in favour of the null hypothesis over all factors.

Overall the profiles are coincident from a socio-demographic perspective.

This is not the case when viewing the results from an organisational point of view. This

result points out that the population of managers differs from the population of

employees, which are in line with hypothesis stating that there are differences to

consider.

We have seen in this study that the effect from leadership in an employee

engagement context is quite evident, which is also in line with other theories (EFQM,

2011; Shingo Prize; 2011, Baldridge, 2009-2010). We have also seen that there are

differences between, for instance, genders and age-groups; however, there appears not

to be a clear pattern in this regard, but is to some extent in line with previous types of

research concerning these demographic parameters (Clark et al., 1996; Wharton et al.,

2000; Eskildsen et al., 2003).

From an analytical point of view there are some implications to be

considered in a set-up such as the one present here;

1. Industrialised data; the constraints of only being able to study data collected in

the industrialised parts of the countries included here, i.e. where we have

internet penetration among the employed populations, might bias the results.

2. Definition of Senior Management; the definition of Senior Management has not

been clear set in the data collected here. This might impose a mix of “who” the

respondents are referring to when giving their answer to questions in this block,

which might bias the results in calculating the effects.

3. Cultural differences; to be able to generalise the results from an analysis such as

pursued here, the author emphasize further studies being undertaken to

investigate especially the socio-demographic and organisational characteristics

(manager vs. employees) on a wider scope of countries.

From an organisational perspective, it is crucial to have “leaders who leads” and from

an employee engagement perspective it is important to have results from an employee

- 107 -

survey pointing in an even stronger direction towards “how” to use different layers of

leadership in order to receive the utmost effect to raise employee satisfaction. A set-up

such as the one presented and analysed here gives an extra view on what and how large

an effect the leaders might pose on factors closely related to the employees such as

Cooperation. This gives added value in the improvement work being conducted within

an organisation, based on results from employee engagement surveys.

Due to the implications in data and the constraint of only being able to

focus on three of the Nordic countries more in-depth, further research should be

undertaken in order to generalise the findings in this study even more.

- 108 -

- 109 -

3.6 References

Baker, W.K. (1995), Allen and Meyer’s 1990 longitudinal study: a reanalysis and

reinterpretation using structural equation modelling. Human Relations, 48(2), 169-186.

Baldridge (2009-2010) Criteria for Performance Excellence, the Baldrige National

Quality, Program at the National Institute of Standards and Technology in

Gaithersburg, MD. Downloaded in March 2011

http://www.baldrige.nist.gov/PDF_files/2009_2010_Business_Nonprofit_Criteria.pdf

Budescu, D. V. (1993). Dominance analysis: A new approach to the problem of relative

importance of predictors in multiple regression. Psychological Bulletin, 114(3), 542-

551.

Chilsehe, N., Haupt, T.C. (2009) The effect of age on the job satisfaction of

construction workers. Journal of Engineering, Design and Technology, 8(1), 107-118.

Chin, W.W. (1998) Commentary: issues and opinion on structural equation modelling,

MIS Quarterly, 22, pp. vii-xvi.

Clark, A., Oswald, A. and Warr, P. (1996) Is job satisfaction U-shaped in age? Journal

of Occupational and Organizational Psychology, 69, 57-81.

Darlington, R. B. (1968) Multiple regression in psychological research and practice.

Psychological Bulletin, 69(3), 161-182.

de Jonge, J., Dormann, C., Janssen, P.P.M., Dollard, M.F., Landeweerd, J.A. & Nijhuis,

F.J.N. (2001), Testing reciprocal relationships between job characteristics and

psychological well-being: a cross-lagged structural equation model. Journal of

Occupational and Organisational Psychology, 74, 29-46.

Deaux, K. and Major, B. (1987) Putting Gender into Context: An Interactive Model of

Gender-Related Behaviour. Psychological Review, 94(3), 369-389.

- 110 -

Dorfman, P. W. (1996). International and cross-cultural leadership research. In B. J.

Punnett, & O. Shenkar (Ed.), Handbook for international management research (pp.

267–349). Oxford, UK: Blackwell.

Eby, L. T., Freeman, D. M., Rush, M. C., & Lance, C. E. (1999). Motivational bases of

affective commitment: a partial test of an integrative theoretical model. Journal of

Occupational and Organizational Psychology, 72, 463–483.

EFQM (2011) Introducing the EFQM Excellence Model Downloaded in March 2011

http://www.efqm.org/en/PdfResources/Introducing%20the%20

Englehart, M. D. (1936) The technique of path coefficients. Psychometrika, 1(4), 287-

293.

Eskildsen, J.K. and Dahlgaard, J.J. (2000), A causal model for employee satisfaction,

Total Quality Management, 11(8), 1081-1094.

Eskildsen, J. K., Kristensen K. & Westlund A. H. (2003) Work motivation and job

satisfaction in the Nordic countries. Employee Relations, 26(2), 122-136.

Eskildsen, J. K., Kristensen K. & Westlund A. H. (2004), Measuring Employee Assets-

the Nordic Employee Index. Business Process Management Journal 10(5), 537-550.

Fornell, C. & Bookstein, F.L. (1982) Two structural equation models: LISREL and PLS

applied to consumer exit-voice theory. Journal of Marketing Research, 19(4), 440-452.

Fornell, C. & Cha, J. (1994) Partial least squares. In: R.P.Bagozzi (Ed.) Advanced

Methods in Marketing Research (pp.52-78). Cambridge, MA: B. Blackwell.

Grömping, U. (2007) Estimators of Relative Importance in Linear Regression Based on

Variance Decomposition. The American Statistician, 61(2), 139-147.

Hoffman, P. J. (1960) The paramorphic representation of clinical judgment.

Psychological Bulletin, 57(2), 116-131.

- 111 -

House, R. J., Hanges, P. J., Ruiz-Quintanilla, S. A., Dorfman, P. W., Javidan, M.,

Dickson, M., et al. (1999). Cultural influences on leadership and organizations: Project

GLOBE. In W. H. Mobley (Ed.), Advances in global leadership (pp. 171–233), 1.

Stamford, CT: JAI Press.

House, R. J. (2004) Culture, Leadership, and Organizations: The GLOBE Study of 62

Societies, SAGE Publications, Thousand Oaks.

Johnson, R.A., & Wichern, D.W., (1992) Applied Multivariate Statistical Analysis, 3rd

ed. New Jersey: Prentice Hall, Inc.

Jordan, PJ & Troth, AC 2011, Emotional intelligence and leader member exchange: The

relationship with employee turnover intentions and job satisfaction, Leadership and

Organization Development Journal, 32(3), 260-280.

Kaplan, R. S. & Norton, D. (1996) The Balanced Scorecard. Boston: Harvard

University Press.

Kristensen, K. & Westlund, A.H. (2001), Management and external disclosure of

intangible assets. European Quality, 8(4), 60-64.

Kristensen, K., Juhl, H.J. & Eskildsen, J.K. (2003), Models that matter. International

Journal on Business Performance Management, 5(1), 91-106.

Kristensen, K. & Westlund, A. (2004). Performance Measurement and Business Results,

Total Quality Management, 15(5-6), 719-733.

Kruskal, W. (1987), Relative Importance by Averaging over Orderings. The American

Statistician, 41(1), 6-10.

Kruskal,W. & Majors, R. (1989). Concepts of relative importance in recent scientific

literature. American Statistician, 43(1), 2-6.

- 112 -

Lohmöller, J-B (1989) Latent Variable Path Modeling with Partial Least Squares.

Heidelberg: Physica.

Pratt, J.W. (1987) Dividing the indivisible: using simple symmetry to partition variance

explained. Proc. Second International Tampere Conference in Statistics (Tampere,

Finland, 1-4 June 1987), Dept. of Mathematical Sciences, Univ. of Tampere, (pp. 245-

260).

Riketta, M. (2005), Organizational identification: a meta-analysis. Journal of

Vocational Behavior, 66(2), 358-384.

Riketta, M. & van Dick, R. (2005), Foci of attachment in organizations: a meta-analytic

comparison of the strength and correlates of workgroup versus organizational

identification and commitment. Journal of Vocational Behavior, 67(3), 490-510.

Shingo Prize (2011) Model & Application Guidelines Downloaded in March 2011

http://shingoprize.org/files/uploads/ShingoModelGuidelines.pdf

Tajfel, H. (1981), Human Groups and Social Categories: Studies in Social Psychology.

Cambridge: Cambridge University Press.

Tenenhaus, M., Vinzi, V. E., Chatelin, Y-M. & Lauro, C. (2005) PLS path modeling.

Computational Statistics and Data Analysis, 48(1), 159 – 205.

Thomas, D.R., & Decady, Y.J. (1999). Point and interval estimates of the relative

importance of variables in multiple linear regression. Unpublished manuscript, Canada

Ottawa: Carleton University.

Van Dick, R., & Schuh, S.C., (2010) My boss’ group is my group: experimental

evidence for the leader-follower identity transfer. Leadership & Organization

Development Journal, 31(6), 551-563.

Vilares, M.J., Almeida, M.H. & Coelho, P.S. (2005) Comparison of likelihood and PLS

estimators for structural equation modelling. A simulation with customer satisfaction

data. Technical Report. New University of Lisbon.

- 113 -

Wharton, A.S., Rotolo, T. and Bird, S.R. (2000), Social context at work: a multilevel

analysis of job satisfaction. Sociological Forum, 15(1), 65-90.

Westlund, A.H., Källström, M. & Parmler, J. (2008) SEM Based Customer Satisfaction

Measurement; On Multicollinearity and Robust PLS Estimation. Total Quality

Management and Business Excellence, 19(7-8), 855-869.

Williams, L.J., Edwards, J.R. & Vandenberg, R.J. (2003) Recent Advances in Causal

Modeling Methods for Organisational and Management Research. Journal of

Management, 29(6), 903-936.

Wold, H. (1985) Partial Least Squares. In: S. Kotz & N. Johnson (Eds), Encyclopedia of

Statistical Sciences (Vol. 6, pp. 581 – 591). New York: Wiley.

Yukl, Gary (2002). Leadership in Organizations. Fifth Edition. Upper Saddle River, NJ:

Prentice Hall.

- 114 -

- 115 -

Appendix A3.1: Results on Relative effects and Relative importance for specified analysis set-up in A) and B)

A) Relative effects and relative importance on Country level, over 4 years’ time

(2007-2010).

Relative Effects:

Year Country

Relative effect on each factor, based on SM!

Model

fit R^2 Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

2007 Brazil 83% 53% 71% 80% 73% 71%

2008 Brazil 95% 69% 64% 63% 70% 76%

2009 Brazil 86% 84% 71% 88% 86% 69%

2010 Brazil 77% 77% 50% 66% 82% 57%

2009 Chile 75% 73% 73% 78% 79% 65%

2010 Chile 97% 70% 63% 74% 64% 64%

2007 China 92% 57% 66% 56% 67% 77%

2008 China 85% 36% 70% 66% 67% 79%

2009 China 87% 67% 69% 76% 72% 58%

2010 China 82% 70% 56% 73% 71% 73%

2007 Czech Republic 82% 54% 51% 64% 74% 71%

2008 Czech Republic 66% 42% 51% 76% 56% 74%

2009 Czech Republic 73% 68% 56% 76% 53% 61%

2010 Czech Republic 68% 64% 69% 70% 68% 64%

2007 Denmark 74% 56% 60% 67% 54% 71%

- 116 -

2008 Denmark 83% 57% 57% 73% 52% 72%

2009 Denmark 90% 55% 61% 68% 53% 63%

2010 Denmark 83% 65% 70% 81% 66% 61%

2007 Estonia 73% 58% 64% 88% 65% 76%

2008 Estonia 75% 67% 60% 60% 66% 71%

2009 Estonia 99% 72% 81% 86% 85% 58%

2010 Estonia 100% 71% 87% 77% 79% 67%

2007 Finland 88% 47% 68% 75% 77% 70%

2008 Finland 81% 72% 66% 84% 55% 75%

2009 Finland 88% 46% 79% 56% 76% 65%

2010 Finland 78% 36% 62% 58% 63% 70%

2007 France 85% 58% 61% 93% 73% 73%

2008 France 81% 37% 56% 76% 73% 74%

2009 France 83% 64% 67% 74% 75% 71%

2010 France 97% 58% 62% 80% 74% 63%

2007 Germany 97% 48% 73% 67% 70% 80%

2008 Germany 91% 58% 63% 64% 61% 75%

2009 Germany 79% 62% 64% 71% 66% 63%

2010 Germany 90% 52% 51% 47% 71% 57%

2007 India 89% 63% 70% 58% 75% 81%

2008 India 91% 39% 38% 59% 64% 76%

2009 India 70% 71% 60% 69% 65% 54%

2010 India 59% 63% 71% 82% 83% 51%

2007 Ireland 89% 49% 59% 87% 65% 74%

2008 Ireland 80% 60% 65% 73% 70% 78%

- 117 -

2009 Ireland 81% 62% 62% 80% 68% 69%

2010 Ireland 89% 60% 62% 60% 65% 70%

Year Country

Relative effect on each factor, based on SM!

Model

fit R^2 Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

2007 Italy 89% 49% 66% 76% 68% 76%

2008 Italy 81% 53% 44% 55% 71% 75%

2009 Italy 85% 85% 91% 65% 73% 71%

2010 Italy 70% 63% 52% 73% 63% 72%

2007 Japan 94% 48% 70% 84% 75% 70%

2008 Japan 83% 55% 73% 79% 76% 76%

2009 Japan 76% 42% 65% 84% 81% 69%

2010 Japan 86% 56% 70% 88% 66% 65%

2009 Mexico 69% 57% 56% 70% 72% 59%

2010 Mexico 78% 78% 66% 93% 77% 62%

2007 Netherlands 88% 68% 52% 92% 63% 75%

2008 Netherlands 81% 50% 59% 69% 60% 72%

2009 Netherlands 84% 67% 54% 71% 54% 57%

2010 Netherlands 90% 52% 37% 100% 75% 69%

2007 Norway 86% 56% 64% 78% 60% 69%

2008 Norway 84% 52% 54% 75% 53% 70%

2009 Norway 91% 59% 64% 71% 55% 67%

2010 Norway 86% 58% 65% 82% 64% 67%

2007 Poland 92% 73% 42% 77% 88% 72%

- 118 -

2008 Poland 100% 55% 66% 69% 71% 72%

2009 Poland 87% 66% 58% 90% 57% 64%

2010 Poland 76% 83% 75% 81% 72% 63%

2007 Russia 87% 64% 72% 81% 66% 66%

2008 Russia 77% 87% 48% 47% 41% 66%

2009 Russia 94% 37% 70% 85% 81% 63%

2010 Russia 98% 59% 64% 91% 59% 57%

2007 Spain 92% 48% 64% 83% 62% 77%

2008 Spain 78% 56% 67% 62% 73% 74%

2009 Spain 74% 53% 65% 82% 70% 71%

2010 Spain 92% 70% 91% 79% 79% 61%

2007 Sweden 85% 64% 74% 80% 71% 70%

2008 Sweden 86% 60% 60% 75% 61% 68%

2009 Sweden 92% 67% 68% 74% 64% 68%

2010 Sweden 91% 63% 73% 78% 66% 68%

2007 United Kingdom 81% 47% 61% 79% 63% 76%

2008 United Kingdom 72% 61% 65% 86% 76% 76%

2009 United Kingdom 89% 65% 58% 77% 67% 71%

2010 United Kingdom 98% 63% 70% 83% 70% 72%

2007 USA 91% 71% 61% 95% 75% 79%

2008 USA 88% 51% 65% 89% 62% 79%

2009 USA 98% 82% 59% 67% 83% 69%

2010 USA 82% 72% 57% 73% 64% 68%

Table A3.1.1 Relative effects between SM and IM, where relative effects are calculated according to

- 119 -

Relative Importance:

Year Country

Relative importance on each factor, based on

SM!

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

2007 Brazil 86% 52% 73% 84% 75%

2008 Brazil 96% 72% 67% 66% 74%

2009 Brazil 88% 86% 74% 91% 90%

2010 Brazil 79% 80% 50% 68% 85%

2009 Chile 80% 78% 77% 83% 84%

2010 Chile 97% 71% 62% 74% 64%

2007 China 93% 54% 65% 54% 66%

2008 China 88% 34% 72% 70% 70%

2009 China 88% 68% 71% 78% 75%

2010 China 83% 70% 55% 73% 71%

2007 Czech Republic 87% 57% 54% 70% 79%

2008 Czech Republic 73% 44% 54% 83% 61%

2009 Czech Republic 78% 73% 58% 82% 55%

2010 Czech Republic 73% 67% 73% 74% 72%

2007 Denmark 78% 57% 62% 70% 54%

2008 Denmark 87% 57% 57% 77% 52%

2009 Denmark 93% 56% 63% 71% 53%

- 120 -

2010 Denmark 86% 67% 72% 84% 68%

2007 Estonia 77% 60% 67% 92% 69%

2008 Estonia 80% 71% 63% 63% 70%

2009 Estonia 100% 73% 83% 88% 86%

2010 Estonia 100% 75% 90% 81% 83%

2007 Finland 91% 43% 70% 78% 81%

2008 Finland 85% 75% 69% 87% 56%

2009 Finland 90% 45% 82% 56% 79%

2010 Finland 80% 31% 62% 56% 63%

2007 France 89% 57% 61% 96% 76%

2008 France 84% 34% 57% 78% 76%

2009 France 84% 63% 67% 75% 76%

2010 France 98% 56% 61% 83% 76%

2007 Germany 98% 47% 77% 71% 73%

2008 Germany 93% 58% 63% 65% 62%

2009 Germany 82% 62% 65% 74% 67%

2010 Germany 92% 51% 51% 45% 73%

2007 India 93% 63% 72% 57% 78%

2008 India 93% 34% 32% 56% 62%

2009 India 72% 74% 62% 72% 68%

2010 India 61% 66% 75% 86% 87%

2007 Ireland 92% 47% 60% 91% 68%

2008 Ireland 84% 61% 66% 76% 72%

2009 Ireland 85% 64% 63% 83% 71%

2010 Ireland 93% 63% 65% 62% 69%

- 121 -

Year Country

Relative importance on each factor, based on

SM!

Reputa-

tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

2007 Italy 92% 46% 67% 79% 70%

2008 Italy 83% 51% 41% 54% 73%

2009 Italy 90% 88% 93% 67% 76%

2010 Italy 73% 65% 53% 77% 65%

2007 Japan 97% 46% 74% 89% 80%

2008 Japan 87% 53% 75% 82% 79%

2009 Japan 79% 37% 65% 87% 84%

2010 Japan 88% 54% 71% 90% 66%

2009 Mexico 71% 58% 58% 74% 75%

2010 Mexico 82% 81% 68% 95% 81%

2007 Netherlands 91% 69% 47% 95% 63%

2008 Netherlands 84% 48% 59% 71% 60%

2009 Netherlands 87% 69% 54% 75% 54%

2010 Netherlands 92% 48% 32% 100% 77%

2007 Norway 88% 55% 64% 80% 60%

2008 Norway 86% 50% 52% 77% 51%

2009 Norway 93% 58% 65% 73% 54%

2010 Norway 88% 58% 65% 85% 65%

2007 Poland 93% 76% 39% 80% 90%

2008 Poland 100% 57% 70% 73% 76%

- 122 -

2009 Poland 89% 69% 59% 93% 59%

2010 Poland 80% 86% 78% 85% 75%

2007 Russia 92% 70% 78% 86% 73%

2008 Russia 80% 91% 46% 45% 37%

2009 Russia 97% 33% 75% 89% 86%

2010 Russia 99% 61% 65% 93% 59%

2007 Spain 94% 45% 65% 87% 63%

2008 Spain 81% 54% 68% 61% 75%

2009 Spain 77% 53% 67% 85% 72%

2010 Spain 93% 72% 93% 81% 81%

2007 Sweden 89% 65% 77% 83% 74%

2008 Sweden 89% 60% 60% 78% 61%

2009 Sweden 94% 68% 69% 77% 65%

2010 Sweden 93% 64% 75% 81% 67%

2007

United

Kingdom 86% 45% 63% 83% 66%

2008

United

Kingdom 75% 62% 67% 90% 80%

2009

United

Kingdom 91% 66% 59% 81% 69%

2010

United

Kingdom 98% 64% 73% 86% 72%

2007 USA 92% 72% 61% 96% 77%

2008 USA 89% 49% 65% 90% 62%

2009 USA 99% 85% 59% 69% 86%

2010 USA 83% 74% 57% 74% 64%

- 123 -

Table A3.1.2 Relative importance, based on SM, on each factor calculated according to

B) Relative effects and relative importance on Continents in 5 parts of the world,

over 4 years’ (2007-2010).

Relative Effects:

Table A3.1.3 Relative effects between SM and IM, where relative effects are calculated according to

Reputa-tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

China & India 2007 88% 59% 66% 57% 70% 79%

2008 88% 37% 53% 64% 66% 77%

2009 77% 72% 64% 72% 68% 56%

2010 67% 68% 62% 74% 75% 62%

Europe 2007 83% 57% 64% 77% 64% 70%

2008 83% 57% 58% 73% 59% 70%

2009 88% 61% 65% 74% 62% 66%

2010 87% 63% 69% 79% 67% 66%

Japan 2007 94% 48% 70% 84% 75% 70%

2008 83% 55% 73% 79% 76% 76%

2009 76% 42% 65% 84% 81% 69%

2010 86% 56% 70% 88% 66% 65%

South America 2007 83% 53% 71% 80% 73% 71%

2008 95% 69% 64% 63% 70% 76%

2009 76% 69% 67% 78% 78% 64%

2010 84% 76% 59% 77% 74% 62%

USA / 2007 91% 71% 61% 95% 75% 79%

North America 2008 88% 51% 65% 89% 62% 79%

2009 98% 82% 59% 67% 83% 69%

2010 82% 72% 57% 73% 64% 68%

Model fit R^2Country YearRelative effect on each factor, based on SM!

- 124 -

Relative Importance:

Table A3.1.4 Relative importance, based on SM, on each factor calculated according to

Reputa-tion

Coop-

eration

Daily

Work

Remune-

ration

Develop-

ment

China & India 2007 90% 58% 66% 55% 71%

2008 90% 33% 52% 64% 66%

2009 79% 74% 65% 74% 70%

2010 68% 70% 63% 76% 77%

Europe 2007 87% 58% 66% 81% 66%

2008 86% 57% 58% 77% 59%

2009 91% 62% 66% 76% 63%

2010 90% 64% 71% 82% 69%

Japan 2007 97% 46% 74% 89% 80%

2008 87% 53% 75% 82% 79%

2009 79% 37% 65% 87% 84%

2010 88% 54% 71% 90% 66%

South America 2007 86% 52% 73% 84% 75%

2008 96% 72% 67% 66% 74%

2009 80% 73% 70% 82% 82%

2010 86% 78% 59% 79% 76%

USA / 2007 92% 72% 61% 96% 77%

North America 2008 89% 49% 65% 90% 62%

2009 99% 85% 59% 69% 86%

2010 83% 74% 57% 74% 64%

Country YearRelative Importance on each factor, based on SM!

- 125 -

Appendix A3.2: Results on Profile analysis - Nordic countries

Test 3.1) Profile analysis – Gender:

Table A3.2.1 Estimated , profile testing for Gender – in the Nordic countries, over four years’

time. A star (*) indicates a significant difference between genders.

Parallel Coincident Level

Test 1 - T2 Test2 - T2 Test3 - T2

Reputation 13.04* 7.00 28.34*

Cooperation 51.90* 5.84 101.57*

Daily Work 34.08* 6.71 19.59*

Remuneration 20.41* 14.39* 88.59*

Development 13.14* 0.05 28.58*

Reputation 10.96* 13.72* 11.01*

Cooperation 14.47* 8.74* 31.01*

Daily Work 2.20 5.09 11.37*

Remuneration 23.41* 29.43* 60.20*

Development 18.59* 0.00 7.56

Reputation 5.15* 6.62 28.07*

Cooperation 70.22* 1.22 118.74*

Daily Work 6.55 6.69 39.22*

Remuneration 1.94 0.72 19.15*

Development 4.42 0.23 41.42*

No

rway

Swe

de

nD

en

mar

k

- 126 -

Test 3.2) Profile analysis – Age-groups:

Parallel Coincident Level

Test 1 - T2 Test2 - T2 Test3 - T2

Cooperation 18 - 29 30 - 39 34.21* 2.1 32.32*

30 - 39 40 - 49 37.86* 6.44 113.45*

40 - 49 50 - 59 18.99* 40.35* 57.89*

50 - 59 60 - 28.60* 0 24.43*

Development 18 - 29 30 - 39 0.76 0.31 9.755*

30 - 39 40 - 49 6.16 0.03 29.84*

40 - 49 50 - 59 25.47* 0.64 19.48*

50 - 59 60 - 10.11* 0.78 33.68*

Daily Work 18 - 29 30 - 39 21.68* 1.36 52.18*

30 - 39 40 - 49 13.74* 1.29 49.93*

40 - 49 50 - 59 17.02* 0.01 2.92

50 - 59 60 - 7.05 5.00 45.96*

Remuneration 18 - 29 30 - 39 38.50* 5.77 1.34

30 - 39 40 - 49 39.07* 0.14 236.40*

40 - 49 50 - 59 1.57 0.29 17.45*

50 - 59 60 - 5.82 3.78 26.03*

Reputation 18 - 29 30 - 39 1.33 0.99 20.19*

30 - 39 40 - 49 12.44* 2.8 15.97*

40 - 49 50 - 59 83.95* 1.76 83.78*

50 - 59 60 - 34.33* 8.011* 319.83*

Cooperation 18 - 29 30 - 39 11.01* 18.01* 26.59*

30 - 39 40 - 49 21.86* 6.45 7.63

40 - 49 50 - 59 20.49* 0.21 51.47*

50 - 59 60 - 33.64* 3.51 9.928*

Development 18 - 29 30 - 39 15.63* 4.61 44.40*

30 - 39 40 - 49 5.7 2.78 10.87*

40 - 49 50 - 59 5.11 1.29 25.01*

50 - 59 60 - 2.24 2.21 5.03

Daily Work 18 - 29 30 - 39 6.82 16.12* 39.26*

30 - 39 40 - 49 10.77* 7.46 8.730*

40 - 49 50 - 59 7.56 0.26 33.58*

50 - 59 60 - 11.22* 9.014* 5.77

Remuneration 18 - 29 30 - 39 16.71* 0.4 22.40*

30 - 39 40 - 49 15.69* 17.37* 95.66*

40 - 49 50 - 59 14.97* 5.42 30.26*

50 - 59 60 - 3.47 5.01 10.89*

Reputation 18 - 29 30 - 39 1.49 19.17* 9.761*

30 - 39 40 - 49 13.34* 3.54 17.32*

40 - 49 50 - 59 30.88* 19.48* 39.59*

50 - 59 60 - 7.62 22.52* 20.43*

De

nm

ark

No

rway

Age groups tested

- 127 -

Table A3.2.2 Estimated , profile testing for age-groups – in the Denmark and Norway, over four

years’ time. A star (*) indicates a significant difference between age-groups.

Table A3.2.3 Estimated , profile testing for age categorized – in the Sweden, over four years’ time.

A star (*) indicates a significant difference between age groups.

Test 3.3) Profile analysis - Managers vs. Employees:

Parallel Coincident Level

Test 1 - T2 Test2 - T2 Test3 - T2

Cooperation 18 - 29 30 - 39 3.96 4.82 6.46

30 - 39 40 - 49 20.19* 0.05 28.28*

40 - 49 50 - 59 49.56* 0.38 48.09*

50 - 59 60 - 35.32* 23.73* 50.14*

Development 18 - 29 30 - 39 2.6 0.02 2.14

30 - 39 40 - 49 0.48 0.07 17.81*

40 - 49 50 - 59 2.5 0.81 17.81*

50 - 59 60 - 9.230* 0.79 18.35*

Daily Work 18 - 29 30 - 39 11.94* 0.03 42.70*

30 - 39 40 - 49 3.06 13.12* 75.49*

40 - 49 50 - 59 44.79* 36.67* 26.98*

50 - 59 60 - 101.02* 20.62* 113.00*

Remuneration 18 - 29 30 - 39 5.07 1.07 36.41*

30 - 39 40 - 49 3.88 0.81 9.844*

40 - 49 50 - 59 79.13* 1.31 26.15*

50 - 59 60 - 29.49* 59.26* 234.8*

Reputation 18 - 29 30 - 39 - - -

30 - 39 40 - 49 31.32* 11.73* 40.36*

40 - 49 50 - 59 - - -

50 - 59 60 - - - -

Swe

de

n

Age groups tested

- 128 -

Table A3.2.4 Estimated , profile testing for managers vs. employees – in the Nordic countries,

over four years’ time. A star (*) indicates a significant difference between managers and employees.

Parallel Coincident Level

Test 1 - T2 Test2 - T2 Test3 - T2

Reputation 4.93 9.43* 60.95*

Cooperation 38.56* 14.60* 127.89*

Daily Work 117.89* 4.89 385.06*

Remuneration 13.28* 11.85* 173.58*

Development 6.69 6.08 3.13

Reputation 5.13 0.10 23.40*

Cooperation 24.64* 25.74* 92.64*

Daily Work 12.07* 12.01* 116.73*

Remuneration 5.71 53.39* 126.02*

Development 14.56* 0.82 115.93*

Reputation - - -

Cooperation 34.76* 5.66 212.73*

Daily Work 25.67* 14.46* 233.38*

Remuneration 16.06* 25.95* 97.97*

Development 8.00* 0.36 71.01*

De

nm

ark

No

rway

Swe

de

n

- 129 -

CHAPTER 4: Psychological profiling in Employee

Engagement Surveys

Mari Källström

Aarhus University

- 130 -

- 131 -

4.1 Introduction

FBI created a system for profiling suspects in criminal acts back in the sixties. Profiling

in this regard is used as a method to narrow down the suspects of interest, for instance

in a murder investigation. You then create a mapping of the crime itself including

gathering of different crime scene information, autopsy report etc. to be able to find a

starting point in the profiling process. Next step is to go deeper in the profiling stage

where you try to “get to know” the type of person committing the specific crime and by

that coming to an understanding of the scenario. At last end a profile describing the type

of person that is most likely to have been committing the crime is developed (Douglas

et al., 1986).

Most often the word profiling is affiliated with police investigations

similar to the case above, however profiling is used in a numerous of ways with a

common goal – to be able to categorise and structure people into subsets and understand

the differences between these subsets of people, which could be marked as types, of

persons out from gender, age, racial, psychological aspects and the behavior from

different perspectives as well as the different interaction of the areas. A statistical term

that could be related, not a synonym, to this area is “clustering”.

Defining structures of data is a common interest in many sciences. A task

in such a process is to define subsets of data that are homogeneous within a group and

to that find a higher level of heterogeneity (in) between groups in the same data set

(Hair et al., 1998). Grouping data can be either on observations or variables. For

grouping of variables, more known as data reduction, there are some multivariate

statistical methods at hand.

A well-known multivariate method for grouping variables is factor

analysis. Factor analysis can be used in two ways; i) exploratory or ii) confirmatory.

These two methods have a common goal and that is to reduce the number of variables in

a defined data set into a smaller set, i.e. grouping variables into a fewer set of variables,

also known as latent variables, by trying to explain as much of the covariance between

the observed variables. This technique is based on Spearmans work in the beginning of

- 132 -

the twentieth century (Spearman, 1904). For further reading on Factor Analysis the

author refers to Bollen (1989), Jöreskog (1979a), Jöreskog (1970), Hair et al. (1998)

among others.

Other methods focusing on reduction of data are FIMIX or REBUS-PLS

to mention two (Hahn et al., 2002; Trinchera, 2007; Vinzi et al., 2008). Neither of these

methods relies on a priori information and the methodology is based on mixture

regression models. FIMIX and REBUS-PLS are both response-based segmentation

techniques used in variance-based structural equation modelling. A distinction between

these two methods is the no-distribution assumption in REBUS-PLS and the basic

procedure in FIMIX relies on Maximum likelihood, which has a normality assumption.

The common approach is to find segments in the responses with heterogeneity in

between in the Path model estimations (Ringle, Squillacciotti & Trinchera, 2007).

Partial Least Squares (PLS) has some similar features with REBUS-PLS;

however, it is statistical method based on multiple regressions and is therefore not a

direct technique for clustering data. For more details of PLS from a theoretical

perspective as well as algorithms, see for instance, Lohmöller (1989); Fornell & Cha

(1994); Tenenhaus, et al. (2005); Vilares, et al. (2005).

A common approach in applying some of the multivariate methods in a

data reduction procedure is to define a model, a structural equation model, where

definitions of link between different latent variables are set. A statistical wording for

this link is a causal relationship.

An area in which there lies an interest of understanding; i) the level of

satisfaction among the employees ii) the drivers of employee satisfaction and iii) the

interaction effect (causality) between the drivers and employee satisfaction and by that

also finding the most cost efficient priorities of what to focus on to achieve higher level

of employee satisfaction, is when analysing the human capital in an organisation. A

possible way of assessing the value of human capital is through Employee Engagement

surveys. The consulting agency, Ennova, conducts employee satisfaction measurements

for organisations internationally where the methodology most often relies on a

Structural Equation Model (SEM), knows as the European Employee Index model (EEI

- 133 -

model) (Eskildsen & Dahlgaard, 2000; Eskildsen et al., 2004). PLS is applied as the

common statistical method when analysing the human capital within Ennova. The

suitability of PLS in employee satisfaction measurements is based on years of research

and many authors have argued that PLS is showing several advantages in comparison to

the covariance based methods (Chin, 1998; Fornell & Bookstein, 1982). There are also

findings from research implying that PLS is robust against statistical implications, such

as; multicollinearity, non-normality and mis-specified models (Cassel et al., 1999, 2000,

2001; Westlund et al., 2008; Källström, 2011).

Within the framework of Ennova, an international survey (European

Employee Index, EEI) is being conducted on an international arena, in total 23 countries

participated in the survey 2011.

The results from an employee engagement analysis conducted as

described above is used in a further interpretation with regards to the effects factors (or

latents) will have, in this case, on employee satisfaction. By means of calculating the

causality between the drivers you will be able to find the general priorities to

concentrate upon in the continuous improvement work from a corporate perspective, i.e.

interpret the results as preferences from the employee point of view.

To use a priori information to classify employees, for instance by use of

demographic variables or common clustering techniques are known alternatives, but

could it be possible to add in an understanding of other parameters or factors that could

add value into this interpretation? One dimension interesting to study, among others, is

the psychological aspects. From a corporate perspective as well as from research point

of view it could be value adding in being able to find a link between the psychological

aspects and the employee preferences to be added in the process of improvement work.

From psychology, we can find a well-known indicator, namely Myer-

Briggs Type Indicator (MBTI). This method is supposed to categorise people into

different types and profiles depending on people’s preferences from a psychological

perspective and also how people perceive the world and make their decisions (Carr et al.,

2011). MBTI is the far most extended method used in psychological typology around

the world (Hirsh & Kummerow, 1989).

- 134 -

The MBTI relies on the typological theory of Jung, which is a theory of an

existing psychological classification in which you will be able to classify people into

different “types” (Jung, 1923). Other typologies based on the Jung approach are

Socionics and Keirsey Temperament Sorter (Augustinavichiute , 1996; Keirsey, 1978).

We can find a number of other methods used in type classification on the market, which

includes JTI, CPI, DiSC among others (see for instance Budd, 1993; Gough & Bradley,

1996). The critique among psychometric researchers regarding the phrasing of “type”

and the interpretation from this is also evident; see for instance Furnham & Crump

(2005) for a specific study in comparing different approaches.

The purpose of this study is to evaluate the impact structure in a structural

equation model in an Employee Engagement context, based on the framework within

Ennova, when; i) analysing the assumed Type-related questions at hand to see if we can

find a difference in impact structure in between the four different types according to the

MBTI and ii) specify the 16 different Jungian profiles based on the questions at hand.

Both perspectives are evaluated based on data collected in 2011 in the independent

Employee Engagement survey, EEI. Data is available for three of the Nordic countries

(Denmark, Sweden and Norway). The aim is therefore to analyse the four psychological

types according to the MBTI together with the well-known classification of these types

into 16 profiles, to see if it could be possible to apply typology in an Employee

Engagement context.

4.2 Myer Briggs Type Indicator

The interest for typology goes back to Carl Jung among others in the field of

psychology. Myer Briggs Type Indicator (MBTI) was initiated in the beginning of the

1940s; however, the starting point in the Briggs family was Katherine Briggs reading

the book Psychological type by Carl Jung (Jung, 1923) and the interest grew to also

influence the daughter Isabel Briggs Myers. Isabel continued the journey of exploring

this field further and the first edition of the MBTI was created as a test for personnel

selection. The main idea was that different work occupations was favoured among

different personality dimensions and that Jung’s theory could be adapted theoretically as

- 135 -

a link between personality and job performance. Today the MBTI tests are applied on a

wide range, for instance among psychologists and counsellors etc. and the aim is to

identify people’s perceptions and the expected effect, i.e. the outcome of different

actions depending on the context for which it is used.

Within the MBTI it is of interest to analyse four different psychological

types together with different pre-defined the combinations of these. The four types are

as follows;

Extrovert (E) --------------------------- Introvert (I), definition of how a person focuses

their attention on the outside world and gathers their energy.

Sensing (S) -------------------------- iNtuition (N), definition of in what way a person

prefers to take in information.

Thinking (T) -------------------------- Feeling (F), defining of in what way a person

prefers to make decisions.

Judgement (J) -------------------------- Perception (P), definition of how a person

orients to the external world – with a judging or perceiving process at hand.

The letter inside brackets is the code for each of the polarised dimension/type. (Lucas,

2007; Ringstad & Odegard, 2002).

The hypothesis is that you cannot be both extremes at the exact same time following the

four types presented above. This is the basic perception within MBTI. A common

approach within the MBTI is to classify individuals into the eight groups, meaning the

eight polarisation possibilities out from the four types. A common approach gathering

information/data is by the pursuit of questionnaires with questions affiliated with each

type asked in a dichotomous way. The questionnaire, most often, includes several

questions being asked per type.

One interest is what type, according to the four dimensions described

above people are categorised into, but the next step is to combine these into profiles.

- 136 -

The 16 different profiles, i.e. output of different combinations out from the four

psychological types, are as follows:

ESTP ESFP ENFP ENTP ESTJ ESFJ ENFJ ENTJ

INTP ISFP INFP INTP ISTJ ISFJ INFJ INTJ

More in depth description of the 16 psychological profiles see for instance, Ringstad &

Odegard (2002).

4.3 Data

European Employee Index (EEI) survey is an annual survey conducted by Ennova in 23

countries (in 2011). The aim is to measure the status on employee satisfaction and

linking generic latents (called drivers) to be able to conclude where the largest effect, or

effects, is in order to raise the satisfaction level among the employees on a national level

(Eskildsen & Dahlsgaard, 2000; Eskildsen et.al., 2003). These drivers are composed of

three to four manifests, i.e. generic questions asked in the survey.

In 2011, a trial was conducted with regards to a psychological angle with

the adding of four questions to the specified questionnaire in the EEI survey assumed to

be related to the four different types in the MBTI, i.e. one question per type. Due to this

we do have some implication known a priori since you will not be able to measure a

dimension in full using only one question. However, it might give input towards further

research within this area of looking at an Employee Engagement context from a

psychological perspective. The four questions included in the survey of 2011 were:

a) I feel comfortable speaking in larger groups of people

This is assumed and will be evaluated if it will add value in the E-I polarisation,

as in high evaluation implying you are more Extrovert and low evaluation,

Introvert.

b) I can remember in detail, when I am retelling a story

- 137 -

This is assumed and will be evaluated if it will add value in the S-N polarisation,

as in high evaluation implying you are more Sensing and low evaluation,

iNtuitive.

c) I perceive myself to be a very emotional-oriented person

This is assumed and will be evaluated if it will add value in the T-F polarisation,

as in high evaluation implying you are more Thinking and low evaluation,

Feeling.

d) I generally prefer to take things as they come instead of making a plan

This is assumed and will be evaluated if it will add value in the J-P polarisation,

as in high evaluation implying you are more Judgmental and low evaluation,

Perceptive.

Within the framework of EEI a Structural Equation Model, based on econometric theory,

is used denoted, the European Employee Index model (EEI model). The EEI model is

presented in Figure 4.1. The statistical method used is partial least squares (PLS), which

is a form of multiple regression to be able to conclude where the most cost efficient

efforts, i.e. effects or impacts, should be placed in order to raise employee satisfaction

and by that also raise the loyalty level within an organisation.

Figure 4.1. The European Employee Index model

Reputation

Senior Management

Immediate Superior

Co-operation

Daily Work

Remuneration

Development

Action areas Result areas

Perception Behaviour

Satisfaction

Motivation

Satisfaction &

MotivationLoyalty

Retention

Commitment

- 138 -

The EEI survey is conducted using web as a main data collection method and CATI is

used to complement the data collection in three of the Nordic countries. The

psychological questions a) through d) above were only asked in Denmark, Sweden and

Norway in the EEI Survey of 2011. In total we have 8129 observations in the three

Nordic countries answering to the four questions specified above.

The most common method to measure profile type among people is the

use of a questionnaire asking questions relating to the four different types in a

dichotomous way. The dichotomy is due to the perception of that you cannot be, for

instance, extrovert and introvert at the exact same time. A difference in this study is that

the four questions above are asked using a ten point scale. From this we are able to look

at the prevalence of people perceiving they are “quite in the middle”, and we will then

be able to conclude if it is so that the impact structure differs substantially whether you

are most certainly one or the other compared to the “middle people” and the low vs.

high scoring on these questions.

4.4 Analysis

The purpose of the study is to add knowledge about psychological types, if possible to

be conveyed, in an Employee Engagement context by using some information based on

the wide-spread method of MBTI. The choice has been to test four questions, each

assumed to be highly related to each of the four types. These questions were included in

the EEI survey of 2011 and we have a total of 8129 responses in three of the Nordic

countries, i.e. Denmark, Sweden and Norway. The analysis will be conducted in two

ways and further on discussed.

In Part A, we will divide the EEI data from 2011 according to the

answering pattern for each question, where initially the following classifications, with

answers on a 1 to 10 scale for each question will be used:

Low – 1, 2, 3 Medium – 4, 5, 6, 7 High – 8, 9, 10

- 139 -

Low, in this case, will be assumed as the far left polarisation on each of the four types

and high will be the assumed opposite polarisation. Medium is merely an extra view on

people not perceiving themselves as being one or the other in terms of preferred action

according to the statements in the questions used as base for this evaluation.

The idea is then to apply PLS as the statistical method and analyse the

impact structures following the set-up of questions included to measure the factors in

the EEI model for each classification. From this we should be able to see if we can find

different impact structure depending on if a person is classified as being one or the other

according to the type categorisation and how this differs, if any, from the polarized

classifications. This will be evaluated on both i) a total data set and ii) the three Nordic

countries separately.

In Part B, after analysing the impact structure, number of observations etc.

we will try to classify the data into the 16 different Jungian profiles and analyse the

impact structure for each of these profiles respectively to see if we can find any

differences with this regard. This will mainly be evaluated out from the whole data set.

Considering this being a trial and not a strict statistical evaluation, the author has chosen

to focus on having large sample, due to the assumption of lowered bias in the estimation

process when increasing sample. The consequence of this ‘choice’ is that we will not be

able to follow a discussion on cultural differences; however it will still give important

insight to the possibilities of profiling in an Employee Engagement context and the

results for each of the 16 psychological profiles for each country, will be presented in

appendix.

The same analytical procedure, as described in Part A, will then be applied

to be able to analyse the impact structure for each profile.

- 140 -

4.5 Results

All results per type and profile will be presented on a relative basis, meaning the actual

effects has been re-calculated to sum up to one hundred percent.

First part will present the results from analysis conducted according to

Part A described under 4.4 above. The impact structure followed by a PLS analysis will

be in focus. A significance analysis in between countries will be further undertaken and

presented at last end of this part.

The consecutive pages will focus on results from an analysis in line with

the set-up denoted Part B, described under 4.4.

Focus will at all times be on impacts between the antecedents and

employee satisfaction following the structural modeling of EEI. This, due to the purpose

of evaluating if differences could be found in effects (i.e. impacts) when data has been

grouped a priori depending on the answering scheme of the four specified psychological

type questions defined under 4.3.

Part A:

At first we have divided the data into three answer-classifications (low, medium, high),

for each question assumed to follow the MBTI. When reviewing the results following a

PLS analysis on the EEI model for each classification/question (on the whole data set,

with no split between countries), the following impact structures are seen;

- 141 -

Table 4.1: Impact structure from a PLS analysis on the EEI model – Low / Medium / High split.

Impact defined as the effect each factor has on Employee Satisfaction & Motivation. Results are

based on whole data with no division of country.

It is clear from the results in Table 4.1 that we can find both similarities and differences

in impact structure based on answering pattern to the four psychological questions.

For the S-N type as well as for the E-I type the largest differences in

impact are for Reputation and Senior Management, where Reputation has a higher

impact for the far left polarisation and the opposite is seen for Senior Management, i.e. a

higher impact for the far right polarisation. Cooperation seems to be yet another area,

where a larger difference can be seen. For both S-N and E-I a higher impact is seen for

those with high evaluation on the question relating to these types compared to the far

left polarization, where the estimated impact is much lower. There are only minor

differences to be seen for the T-F and J-P.

The medium classification shows some differences in relation to the more

polarized definitions of the four types. However, this is not a clear cut image which

might also be a confirmation of the original thinking of these types – that you cannot be

both at the same moment and the perception from the respondents found in this could be

seen as a verification of this assumption. The use of a 1-10 point scale in the

questionnaire implies that the respondents have to take a decision in a specific direction

in answering to these four questions (no middle value). Even though this does not imply

a straight-forward polarisation it is still a matter to consider. We also want to take the

Low evaluation Medium evaluation High evaluation Low evaluation Medium evaluation High evaluation

Reputation 22% 17% 13% 19% 16% 15%

Senior Management 3% 8% 10% 3% 8% 8%

Immediate manager 7% 7% 5% 10% 6% 6%

Cooperation 5% 6% 11% 4% 7% 9%

Daily Work 47% 42% 42% 47% 43% 43%

Remuneration 3% 7% 5% 6% 5% 6%

Development 14% 13% 12% 10% 15% 12%

I feel comfortable speaking in larger groups of people I can remember in detail, when I am retelling a story E-I type S-N type

Low evaluation Medium evaluation High evaluation Low evaluation Medium evaluation High evaluation

Reputation 16% 15% 17% 16% 14% 20%

Senior Management 8% 9% 7% 8% 8% 8%

Immediate manager 11% 4% 8% 7% 6% 6%

Cooperation 3% 11% 6% 7% 10% 4%

Daily Work 43% 42% 44% 44% 42% 46%

Remuneration 6% 5% 6% 6% 5% 5%

Development 13% 14% 13% 12% 15% 11%

T-F type J-P type

I perceive myself to be a very emotional-oriented person I generally prefer to take thing as they come instead of making a plan

- 142 -

number of observations into consideration, since further analysis is aiming at defining

the 16 psychological profiles based on the answering scheme. Due to this, we should

evaluate if we can see a difference in impact structure if we split the data into two parts,

and by that removing the medium classification. The following definition of low versus

high is considered for each question, hereafter named as “two split”:

Low – 1, 2, 3, 4, 5 High – 6, 7, 8, 9, 10

Table 4.2 presents the results from this two split analysis.

Table 4.2: Impact structure from a PLS analysis on the EEI model – Low / High split. Impact

defined as the effect each factor has on Employee Satisfaction & Motivation. Results are based on

whole data with no division of country.

From Table 4.2 we can conclude that we can find differences in impact structure,

mainly on reputation and senior management for E-I and S-N as was the case also with

a three group classification in answering scheme.

Low evaluation High evaluation Low evaluation High evaluation

Reputation 19% 15% 17% 16%

Senior Management 5% 10% 6% 9%

Immediate manager 6% 6% 8% 6%

Cooperation 5% 10% 7% 8%

Daily Work 45% 42% 43% 43%

Remuneration 5% 5% 4% 6%

Development 15% 12% 15% 13%

I feel comfortable speaking in

larger groups of people

I can remember in detail, when I

am retelling a story

E-I type S-N type

Low evaluation High evaluation Low evaluation High evaluation

Reputation 17% 16% 14% 18%

Senior Management 9% 8% 9% 7%

Immediate manager 5% 7% 7% 6%

Cooperation 9% 8% 9% 7%

Daily Work 42% 43% 43% 44%

Remuneration 5% 5% 6% 4%

Development 13% 13% 13% 14%

T-F type J-P type

I perceive myself to be a very

emotional oriented person

I generally prefer to take thing as

they come instead of making a

plan

- 143 -

The above results are indicating differences in impact structure on the

whole data set. Continuing with same set-up (two-split) and split the data into the three

countries being surveyed will show if it is possible to find any cultural differences.

Table 4.3-4.5 presents the two split results per country (Denmark, Norway and Sweden),

for each question included.

Table 4.3: Impact structure from a PLS analysis on the EEI model – Low / High split. Impact

defined as the effect each factor has on Employee Satisfaction & Motivation. Results for Denmark.

Table 4.4: Impact structure from a PLS analysis on the EEI model – Low / High split. Impact

defined as the effect each factor has on Employee Satisfaction & Motivation. Results for Norway.

Table 4.5: Impact structure from a PLS analysis on the EEI model – Low / High split. Impact

defined as the effect each factor has on Employee Satisfaction & Motivation. Results for Sweden.

Low evaluation High evaluation Low evaluation High evaluation Low evaluationHigh evaluation Low evaluationHigh evaluation

Reputation 23% 15% 20% 16% 16% 18% 12% 23%

Senior Management 8% 12% 7% 12% 12% 11% 13% 9%

Immediate manager 7% 8% 10% 7% 6% 8% 8% 6%

Cooperation 1% 8% 4% 6% 4% 6% 4% 6%

Daily Work 46% 43% 46% 44% 45% 44% 46% 43%

Remuneration 7% 4% 7% 4% 7% 4% 4% 5%

Development 9% 10% 6% 11% 9% 10% 12% 7%

I generally prefer to

take thing as they

come instead of

T-F type J-P type

I feel comfortable speaking in

larger groups of people

I can remember in detail, when I

am retelling a story

E-I type S-N type

I perceive myself to be

a very emotional

oriented person

Low evaluation High evaluation Low evaluation High evaluation Low evaluationHigh evaluation Low evaluationHigh evaluation

Reputation 23% 13% 18% 15% 21% 14% 17% 13%

Senior Management 5% 12% 9% 10% 12% 9% 11% 9%

Immediate manager 3% 6% 2% 5% 4% 6% 4% 6%

Cooperation 8% 14% 15% 12% 10% 13% 13% 11%

Daily Work 43% 42% 36% 44% 40% 42% 43% 40%

Remuneration 5% 5% 5% 6% 4% 6% 6% 5%

Development 14% 8% 15% 9% 9% 10% 7% 15%

E-I type S-N type T-F type J-P type

I feel comfortable speaking in

larger groups of people

I can remember in detail, when I

am retelling a story

I perceive myself to be

a very emotional

oriented person

I generally prefer to

take thing as they

come instead of

Low evaluation High evaluation Low evaluation High evaluation Low evaluationHigh evaluation Low evaluationHigh evaluation

Reputation 13% 15% 13% 16% 14% 15% 13% 18%

Senior Management 2% 5% 3% 3% 4% 3% 3% 3%

Immediate manager 7% 5% 10% 5% 6% 7% 8% 4%

Cooperation 5% 8% 4% 8% 10% 6% 8% 5%

Daily Work 48% 41% 46% 43% 42% 44% 41% 48%

Remuneration 4% 6% 2% 6% 5% 6% 8% 2%

Development 20% 19% 22% 18% 19% 20% 19% 21%

E-I type S-N type T-F type J-P type

I feel comfortable speaking in

larger groups of people

I can remember in detail, when I

am retelling a story

I perceive myself to be

a very emotional

oriented person

I generally prefer to

take thing as they

come instead of

- 144 -

From Table 4.3-4.5 it is evident that the impact levels and pattern per type for Norway

and Denmark are quite similar generally, whilst Sweden seem to have a more

differentiated pattern in comparison. Two striking results are Development and Senior

Management. Development seems to have a very high impact on Employee Satisfaction

while Senior Management shows very low impact in Sweden regardless of

psychological type and polarisation. In Denmark and Norway, both the levels of

impacts relating to Development and Senior Management as well as differences

depending on type. Even though the impacts per type seem to be on same level for

several of the seven factors being analysed (Reputation – Development), we cannot

conclude any cultural differences being present without further analysis on the subject.

The results here imply cultural differences being conveyed. The focus is

the impact levels being similar per type and factor between Denmark and Norway

compared to Sweden. To be able to conclude if there are significant differences on the

level of impacts between the countries a simple significance test has been conducted

following a large sample t test, considering the samples being analysed is greater than

30. The test statistic is presented in (4.1).

√(

) (

)

(4.1)

Where se represents Sweden and i=dk, no - representing Denmark and Norway

respectively, since we are firstly interested on a test between Sweden vs. the other two

countries separately. Results from this test are shown in Table 4.6 and 4.7. Significant

differences are represented using a star (*) in both tables.

Table 4.6: Results from a Large sample t-test, Sweden vs. Denmark. Estimated presented in

table.

Low evaluation High evaluation Low evaluation High evaluation Low evaluation High evaluation Low evaluation High evaluation

Reputation -103.47* 3.96* -55.82* -12.52* -17.17* -82.15* -0.60 -72.70*

Senior Management -52.14* -135.82* -27.20* -187.30* -62.03* -153.08* -146.29* -76.94*

Immediate manager -5.05* -62.51* -11.30* -41.17* -2.94* -36.62* -12.64* -37.54*

Cooperation 33.97* 7.94* -3.17* 53.78* 37.74* -7.57* 56.23* -20.17*

Daily Work -25.29* -47.38* -31.19* -35.50* -30.98* -39.55* -98.68* 24.48*

Remuneration -31.60* 45.58* -32.03* 40.59* -19.29* 16.89* 42.60* -42.51*

Development 106.26* 165.52* 86.55* 174.62* 74.75* 192.96* 96.93* 171.70*

I feel comfortable speaking

in larger groups of people

I can remember in detail,

when I am retelling a story

I perceive myself to be a very

emotional oriented person

I generally prefer to take

thing as they come instead

of making a plan

E-I type S-N type T-F type J-P type

- 145 -

Table 4.7: Results from a Large sample t-test, Sweden vs. Norway. Estimated presented in

table

The significance tests are showing significant difference overall, with only four cases in

total departing from this pattern in between the countries (i.e. Sweden vs. Denmark).

The results are implying cultural differences being present, however we have only

conducted a test for each impact separately and no further analysis will be conducted

here in relation to psychological type (between Sweden and Norway / Denmark)

Earlier findings implied similarities of the impact structure in between

Denmark and Norway. Therefore a significance test between these countries (on impact

levels) has been conducted according to (4.1). Table 4.8 presents the result from this test.

As can be seen we do find significant differences on impact levels between all three

Nordic countries generally.

Table 4.8: Results from a Large sample t-test, Denmark vs. Norway. Estimated presented in

table

Low evaluation High evaluation Low evaluation High evaluation Low evaluation High evaluation Low evaluation High evaluation

Reputation -77.44* 32.85* -34.57* 9.96* -46.66* 5.47* -77.37* 46.01*

Senior Management -19.10* -132.41* -33.60* -141.20* -57.85* -118.84* -118.34* -67.96*

Immediate manager 39.21* -7.68* 52.68* -5.14* 21.18* 22.26* 70.27* -29.80*

Cooperation -20.25* -117.64* -63.72* -71.59* 3.38* -150.35* -77.92* -63.59*

Daily Work 26.36* -31.03* 29.36* -25.44* 18.29* -7.59* -54.14* 64.93*

Remuneration -10.41* 12.04* -17.07* 17.75* 7.17* -24.23* 25.58* -33.36*

Development 56.65* 219.23* 37.08* 225.60* 78.56* 196.11* 194.24* 71.09*

E-I type S-N type T-F type J-P type

I feel comfortable speaking

in larger groups of people

I can remember in detail,

when I am retelling a story

I perceive myself to be a very

emotional oriented person

I generally prefer to take

thing as they come instead

of making a plan

Low evaluation High evaluation Low evaluation High evaluation Low evaluation High evaluation Low evaluation High evaluation

Reputation 13.82* 27.90* 14.53* 22.42* -25.07* 83.31* -68.68* 119.35*

Senior Management 22.22* 7.68* -8.21* 44.04* 4.88* 27.64* 25.41* 5.19*

Immediate manager 40.08* 54.42* 54.90* 34.27* 20.97* 55.12* 74.24* 6.48*

Cooperation -45.41* -119.40* -52.43* -120.27* -31.08* -136.55* -119.41* -44.80*

Daily Work 44.42* 18.03* 51.24* 9.89* 44.89* 29.53* 42.50* 41.03*

Remuneration 15.69* -33.43* 10.88* -21.97* 23.83* -39.37* -15.93* 6.46*

Development -34.96* 47.45* -42.66* 52.41* 0.47 7.15* 86.01* -98.44*

I generally prefer to take

thing as they come instead

of making a plan

E-I type S-N type T-F type J-P type

I feel comfortable speaking

in larger groups of people

I can remember in detail,

when I am retelling a story

I perceive myself to be a very

emotional oriented person

- 146 -

Cultural differences when following the MBTI approach has been a subject of research.

It is also evident from a practitioner’s point of view that when working with the MBTI

approach diversities will be evident on an international arena (Kirby, 2007). The results

here also confirm earlier research focusing on cultural differences, but from an

employee engagement perspective. However, due to the Nordic focus we are not able to

provide a global discussion on this but the results do give insight to the possibility of

diversities internationally. More research should therefore be taken into consideration.

A literature study from the author has not revealed any earlier research of

MBTI being taken into consideration within a context presented here. Further research

is therefore very much emphasized.

Part B:

We have earlier stated that we are able to find differences when looking at the four

questions at hand separately. Next step is to investigate the possibility of preparing the

16 profiles associated with the MBTI approach, out from these four questions and study

the impact structure in between these profiles. Considering the number of observations,

we will here focus on the whole data set in preparation of these profiles. Analysis has

been conducted for each country separately as well and the result from this can be found

in appendix.

The profiles have been prepared by combining each polarisation per

psychological type defined earlier to match the profile description presented under

chapter 4.2. The prevalence in the data on each profile is presented in Figure 4.2.

- 147 -

Figure 4.2. Prevalence in percent of the 16 profiles present in the total data set.

As seen in Figure 4.2 there are especially two profiles that are dominated

in the data, namely ESFJ and ESFP, accounting for 43% of the total sample. Looking at

these split per country we find that it is quite similar number of observations in each

country, implying that these two profiles are highly represented in the Nordic countries

generally. Further on we find that ESTJ and ISTJ together are accounting for approx. 18%

of the sample. Figure 4.3 and 4.4 presents the impact structure following a PLS analysis

conducted following the EEI model for each of the 16 profiles on the total data set. The

prevalence and impacts for each of the 16 profiles, following the same analytical

process, for each country separately, are shown in appendix.

- 148 -

Figure 4.3: Impact structure from a PLS analysis on the EEI model for the 8 profiles following

MBTI extrovert definition. Impact defined as the effect each factor has on Employee Satisfaction &

Motivation. Results are based on whole data with no division of country.

Figure 4.4: Impact structure from a PLS analysis on the EEI model for the 8 profiles following

MBTI introvert definition. Impact defined as the effect each factor has on Employee Satisfaction &

Motivation. Results are based on whole data with no division of country.

Focusing on the eight Extrovert defined profiles, the results imply quite similar levels

for Reputation, in particular. Daily Work is, for instance, more scattered which indicate

that the effect on employee satisfaction is more differentiated depending on which

psychological profile the respondents are grouped within, from the Extrovert

- 149 -

perspective. The opposite pattern is shown for the Introvert defined profiles. The effect

on employee satisfaction from Reputation is showing a larger spread, while the effect

from Development is more homogenous among the Introvert profiles. When viewing all

16 profiles, one find that overall there are similarities in pattern, but the size of effects

differs which further implies that the impact structure seem to differ depending on the

psychological profile the respondents are categorized in. The results shows similar

pattern when viewing the three countries separately, as shown in appendix.

4.6 Discussion & Conclusion

The aim with this study was to conduct an analysis of a known employee satisfaction

model with an a priori classification of employees according to the four types known

from MBTI using PLS as the statistical method of estimation. The trial of adding four

questions, one for each type according to the MBTI, in an independent employee

satisfaction survey conducted in three of the Nordic countries during 2011 has been the

base for this evaluation.

The results are showing that we can find some differences in impact

structure depending on the psychological type with significant differences between the

countries at hand. The results are further showing some differences between the 16

profiles defined in the MBTI approach, which has been evaluated on the entire data set

due to the restriction of sample sizes for each of the three Nordic countries.

We are not able to see a clear pattern and questions are raised as to

“why?”. We do have some implications which could or even should have effects.

A common procedure in the MBTI is to use a questionnaire with a larger

number of questions aiming at capturing the four types from a dimensional perspective.

These questions are most often presented as statements where the respondent is asked to

take a stand in either of two directions to each statement. The two directions aim at

capturing the polar for each type (E-I, S-N, T-F, J-P). These types are not only a one

dimension factor, they are more of a unity of several psychological criteria, which

- 150 -

indicate that each type, for anyone used to working with models, could be named as

latents in a structural model. The difference is that the MBTI is not presenting any result

parameter, i.e. the four types are not assumed to have a certain effect on yet another

latent, but instead these four types are very much linked to each other. However, the

likeness of having several parameters/questions aiming at capturing different parts for

each type raises the question: is one question “enough” to be able to draw any stronger

conclusions referring to the MBTI? The answer is very likely to be “no, not entirely”.

This should be seen as a limitation in this study, where we have only one

question assumed to be adding information for each type. However, from this study

where we in one part have looked at the four questions separately we can state that we

can find i) both differences and likeness in impact structure following the PLS analysis

pursued between the low vs. high evaluation for each questions and ii) a significant

difference following the PLS analysis performed for each of the Nordic countries and

thus give some evidence that we have cultural differences. But, the conclusions can only

be drawn taken these specific questions into consideration and because of the fact that

we have only one question per type we are not able to follow the MBTI interpretation

entirely.

Another possible limitation is the use of a 10 grade scale instead of two-

direction statements to each question which is a normal process in MBTI to pursue.

However, research has also indicated that there might be validity and reliability issues

with the standard approach in MBTI, which might pose problems in determining

people’s profiles (Pittenger, 1993). Tieger & Barron-Tieger (1993) argues that a person

does not change his or her profile, i.e. stating that being for instance an ESTJ you will

continue being an ESTJ throughout your life. This has been further evaluated in later

research and even consultants being trained in MBTI argues differently. The possibility

to study people’s perception with regards to these types on a broader scale as has been

the case in this study should be further investigated.

The author has consulted a trained consultant in the MBTI approach with

regards to an evaluation of the questions used in this study. The input received is that

the wordings for question number three might pose some special issues since the

phrasing uses the word “emotional”. According to the consultant, this phrasing will bias

- 151 -

the result for the T-F type since the definition of this type is not about emotions. The

author agrees to this statement.

A conclusion to be drawn is that taking all together the evaluation of the

questions and method used might pose issues with a non-biased evaluation from a

MBTI perspective. The author therefore do recommend further research on this subject,

in terms of using more elaborated questions in total, more questions per type and a

deeper analysis of the use of a 10 point scale.

Due to above statements we can give a sum-up of recommendations as to

what to take into consideration from an analytical point of view;

1. Consideration of what questions to include in order of getting a proper view of

each type, to make sure a validity of the questions.

2. Consider in what context the questions are to be used. In order to prepare for

possibility of profiling, the number of questions to be included for each type

needs to be evaluated.

3. In an attempt of using types or profiles as input to an Employee Engagement

analysis, as pursued here, there should be an evaluation of sample size in order

to secure a proper base for further evaluations.

We also have the recipient of results of this kind, i.e. an organisation. The question is;

why pursue an approach like this in Employee Engagement Measurements? The saying;

“We are different from one another” is true to some part but we also have something in

common as people. Understanding the differences and similarities among groups of

people and identifying the strength within each group has been an area of research and

interest from organisations for years.

The same is true for Employee Engagement surveys, where the

understanding of different challenges in climate in different parts of the organisation is

of high interest. The added value to add psychology as a parameter to address in such a

set-up is the increase in understanding “who” the employees are and should be able to

seek a cost reduction in the improvement work, since the organisation receive added

information that ease the complexity of understanding the differences withheld in the

results. The enhancement from a managerial perspective by receiving a wider and

- 152 -

deeper insight into “who” their employees are, by introducing a psychological

parameter taking “behavior” even more into consideration, also gives an extra tool to

use in their improvement work within their department. Setting wrongly directed

actions might actually increase the cost and could have a negative effect on what they

are trying to pursue.

However, neither psychology as a science or MBTI as a focus area should

be taken lightly. This means that organisations should consult professionals in

interpreting the results, so that the correct analyses of the results are placed at hand.

Another recommendation is that the focus in a context described here should still be set

on the improvement possibilities in the quest of increasing employee satisfaction.

This study has evaluated a psychological perspective and the possibility to

include a wider and deeper background using a psychological approach being added

into the world of Employee Engagement surveys. The result shows that we are able to

find differences which have been shown to give evidence to a deeper understanding

which is useful from several stakeholders’ perspective.

The implications, described earlier, should be further investigated.

Therefore further research should focus on meeting the acquired levels in the set-up,

such as i) adding more questions per type ii) securing a stronger grasp of the usage of a

10 point scale together with iii) a further investigation of cultural differences /

similarities iv) there should also be a focus in interpreting the differences in impacts

structure in order to understanding the link between the profiles and the results followed

by an analysis such as the one pursued here.

Research should also focus on further evaluation of the chosen

psychological perspective used in a context such as this. The author do not recommend

MBTI to be the solely method of choice, but investigation of other methods within the

area of psychology and typology should also be evident together with comparisons in

between in a context such as this.

- 153 -

4.7 References

Augustinavichiute A. (1996). The Socion, or Socionics Basics. Socionics, Mentology,

and Personality Psychology, 4-5.

Bollen, K. A. (1989) Structural Equations with Latent Variables, New York: Wiley.

Budd, R. J. (1993b). Jung Type Indicator: The technical manual. Letchworth: Psytech

Intemational Ltd.

Carr, M., Curd, J., & Dent, F. MBTI Research into Distribution of type. Downloaded in

June 2011.

http://www.ashridge.org.uk/Website/IC.nsf/wFARATT/MBTI%20Research%20into%2

0Distribution%20of%20Type/$file/MyersBriggs.pdf

Cassel, C., Hackl, P., & Westlund, A.H. (1999) PLS for estimating latent variable

quality structures: finite sample robustness properties, Journal of Applied Statistics,

26(4), 435-446.

Cassel, C., Hackl, P., & Westlund, A.H. (2000) On measurement of intangible assets: a

study of robustness of partial least squares. Total Quality Management, 11(7), 897-907.

Cassel, C., Eklöf, J, Hackl, P. & Westlund, A.H. (2001) Structural analysis and

measurement of customer perceptions, assuming measurement and specification errors.

Total Quality Management, 12(7-8), 873-881.

Chin, W.W. (1998) Commentary: issues and opinion on structural equation modelling,

MIS Quarterly, 22, pp. vii-xvi.

Douglas, J.E., Ressler, R.K., Burgess, A.W., & Hartman, C.R.(1986). Criminal profiling

from crime scene analysis. Behavioral Sciences and the Law, 4 (4): 401-421.

Eskildsen, J.K. and Dahlgaard, J.J. (2000), A causal model for employee satisfaction.

Total Quality Management, 11(8), 1081-1094.

- 154 -

Eskildsen, J. K., Kristensen K. & Westlund A. H. (2004), Measuring Employee Assets.

Business Process Management Journal, 10(5), 537-550.

Eskildsen, J.K, Kristensen, K: and Westlund, A.H (2003) Work motivation and Work

satisfaction in the Nordic countries. Employee Relations, 26(2), 122-136.

Fornell, C. & Cha, J. (1994) Partial least squares. In: R.P.Bagozzi (Ed.) Advanced

Methods in Marketing Research (pp.52-78). Cambridge, MA: B. Blackwell.

Fornell, C. & Bookstein, F.L. (1982) Two structural equation models: LISREL and PLS

applied to consumer exit-voice theory. Journal of Marketing Research, 19(4), 440-452.

Furnham, A., & Crump, J. (2005). Personality Traits, Types, and Disorders: An

Examination of the Relationship Between Three Self-Report Measures. European

Journal of Personality, 19(3), 167-184.

Gough,H.G. & Bradley, P. (1996). CPI Manual. Ed.3. Palo Alto, CA: Consulting

Psychologists Press.

Hahn, C., Johnson, M., Herrmann, A., & Huber, F. (2002) Capturing customer

heterogeneity using a finite mixture PLS approach. Schmalenbach Business Review, 54,

243–269.

Hair, J. F., Anderson, R.E., Tatham, R.L. & Black, W.C. (1998) Multivariate Data

Analysis. Prentice Hall Inc. Fifth Edition.

Hirsh, S.K., & Kummerow, J.M. (1989). Life types. New York: Warner Books.

Jung, C.G. (1923). Psychological types. Princeton, NJ: Princeton University Press.

Jöreskog, K.G. (1970) A general method for analysis of covariance structures.

Biometrika, 57(2), 239-251.

Jöreskog, K.G. (1979a) Basic Ideas of factor analysis and component analysis. In K.G.

Jöreskog and D.Sörbom, Advances in Factor Analysis and Structural Equation models

(pp. 5-20). Cambridge, MA: Abt.

- 155 -

Keirsey, D. (1978). Please Understand Me II: Temperament, Character, Intelligence

(1st Ed. ed.). Prometheus Nemesis Book Co.

Kirby, L.K., Kendall, E. & Barger, N.J. (2007) Type and Culture. CPP

Källström, M. (2011) Essays on the Use of PLS Estimation: for Improvement of Non-

Financial Performance Indicators, Ph.D. Dissertation, Department of Business

Administration, Aarhus University, Buiness and Social Sciences, Aarhus

Lohmöller, J-B (1989) Latent Variable Path Modeling with Partial Least Squares.

Heidelberg: Physica.

Lucas, D. J. (2007). Personality Type (MBTI) Relationship to Performance and

Satisfaction in Web-Based Instruction (WBI). Unpublished Doctoral dissertation, North

Carolina State University, Raleigh, NC.

Pittenger, David J. (1993) Measuring the MBTI and Coming Up Short. Journal of

Career Planning & Placement.

Ringle, C. M., Squillacciotti, S. & Trinchera, L. (2007). A Study on Methods for

Capturing and Treating Heterogeneity in PLS Path Models by Unit Segmentation:

FIMIX-PLS, PLS-TPM and REBUS-PLS. PLS'07: 5th International Symposium on

PLS and Related Methods.

Ringstad, H.E. & Ødegård, T (2002) Typeforståelse: Jungs Tyoepsykologi, CFL,

Optimas Organisationspsykologene, Bergen, Norway

Spearman, D. (1904) “General intelligence”, objectively determined and measured.

American Journal of Mathematical and Statistical Psychology, 15(2), 201-292.

Tenenhaus, M., Vinzi, V. E., Chatelin, Y-M. & Lauro, C. (2005) PLS path modeling.

Computational Statistics and Data Analysis, 48, 159 – 205.

Tieger, P.D. & Barron-Tieger, B. (1993) Personality Typing: A First Step to a

Satisfying Career. Journal of Career Planning & Employment, 53(2), 50-56.

Trinchera L.(2007) Unobserved heterogeneity in structural equation models: a new

approach in latent class detection in PLS path modeling. Ph.D. Dissertation,

Department of Mathematics and Statistics, University of Naples, Italy.

Vilares, M.J., Almeida, M.H. & Coelho, P.S. (2005) Comparison of likelihood and PLS

estimators for structural equation modelling. A simulation with customer satisfaction

data. Technical Report. New University of Lisbon.

- 156 -

Vinzi, V.E., Trinchera, L., Squillacciotti, S., & Tenenhaus, M. (2008) REBUS-PLS: A

response-based procedure for detecting unit segments in PLS path modeling Applied.

Stochastic Models Business and Industry, 24, 429-458.

Westlund, A.H., Källström, M. & Parmler, J. (2008) SEM Based Customer Satisfaction

Measurement; On Multicollinearity and Robust PLS Estimation. Total Quality

Management and Business Excellence, 19(7-8), 855-869.

- 157 -

Appendix 4.1: Prevalence and impact structure following MBTI definition in the Nordic countries

Figure A4.1: Prevalence of 16 profiles following MBTI definition – Denmark. Number of

observations lower than 30 is marked with an (*).

Figure A4.2: Prevalence of 16 profiles following MBTI definition – Norway. Number of

observations lower than 30 is marked with an (*).

- 158 -

Figure A4.3: Prevalence of 16 profiles following MBTI definition – Sweden. Number of

observations lower than 30 marked is with an (*).

Figure A4.4: Impact structure from a PLS analysis on the EEI model on the 16 profiles following

MBTI definition. Impact defined as the effect each factor has on Employee Satisfaction &

Motivation. Results are based on data for Denmark.

- 159 -

Figure A4.5: Impact structure from a PLS analysis on the EEI model on the 16 profiles following

MBTI definition. Impact defined as the effect each factor has on Employee Satisfaction &

Motivation. Results are based on data for Norway.

Figure A4.6: Impact structure from a PLS analysis on the EEI model on the 16 profiles following

MBTI definition. Impact defined as the effect each factor has on Employee Satisfaction &

Motivation. Results are based on data for Sweden.

- 160 -

- 161 -

Concluding remarks

The purpose of this dissertation has been to add more knowledge to the use of partial

least squares (PLS) estimation when measuring intangible information with structural

equation models, namely within the field of i) customer satisfaction and ii) employee

satisfaction measurements. The first two chapters have focused on modelling of

customer satisfaction and the last two chapters have evaluated modelling in an

employee satisfaction context. The two frameworks being analysed are the EPSI Rating

model (for customer satisfaction) and EEI model (for employee satisfaction). Both of

these models have been developed through extended research (ECSI, 1998; Fornell,

1992, 2007; Fornell et al., 1996; Williams et al., 2003; Eskildsen et al., 2004). The

statistical method used within each framework is Partial Least Squares (PLS), which is

a variance-based method (Lohmöller, 1989; Wold, 1985; Fornell & Cha, 1994;

Tenenhaus et al., 2005; Vilares et al., 2005). Many authors argue that PLS is showing

several advantages compared to covariance-based methods (Chin, 1998; Fornell &

Bookstein, 1982).

The area of interest in the firsts two chapters have been focused on

analysing effects from i) multicollinearity and ii) skewness on several levels of the

structural parameters, two statistical implications most often seen empirically. The

results here are in favour of PLS, meaning that we are able to conclude that PLS is

robust towards these implications under the conditions limited to the specific models

used for data generation conveyed here.

However, question-marks with regards to the analytical set-up have been

raised during the evaluation process. Further research is therefore much emphasized

with a special focus on; i) evaluation of robustness using models that are evident

empirically, since the simplified models taken into consideration here are practically not

seen in reality ii) the correlation set-up; in these studies a Cholesky transformation has

been used. However, a set-up as such implies the correlations to diminish when adding

factors into the model. This is not a common scenario empirically iii) comparison with

covariance-based methods, for instance LISREL, over the statistical implications

analysed here should also be conveyed in order to have more clear-cut results on argued

- 162 -

advantages in favour of PLS. There are, to the author’s knowledge, very few studies

being conducted on this subject and should therefore be emphasized.

In the continuous search for improved links between theory and reality

validated framework such as the EEI model, should be analysed further. In chapter 3 the

focus has been to rearrange the EEI model in order to study leadership on a deeper level

in an employee engagement context, meaning the in-direct effect on factors linked as

drivers for employee satisfaction. This due to several theoretical perspectives viewing

leadership as ‘driving force’ for business excellence (EFQM, 2011; Shingo Prize, 2011;

Baldridge, 2009-2010). Here we have shown that the effect, evaluated through the

structural parameters, from i) senior management and ii) immediate manager is quite

substantial, especially considering senior management, which implies that organisations

can receive added value in how to proceed with the improvement work to increase

employee satisfaction and the antecedents, from a more ‘hands-on’ managerial

perspective in a set-up presented here. But, further research is highly emphasized, due to

both implications in data presented here and the lack of possibility to take cultural

differences into consideration.

Several studies has shown that the use of PLS in Structural Equation

Modelling is a good option in analysing factors that are considered not possible to

measure directly such as satisfaction and it’s antecedents (drivers) (Williams et al.,

2003; Eskildsen et al., 2004; Chin, 1998; Fornell & Bookstein, 1982, Fornell, 1992;

Fornell et al., 1996; Fornell, 2007). Earlier research has argued that there are differences

in employee satisfaction depending on age and/or gender (Clark et al., 1996; Wharton et

al., 2000; Eskildsen et al., 2003), which is useful information from an organisational

perspective, due to the possibility to constrain actions with an even stronger analytical

base.

Being able to go even further in depth in structuring data, analyse it and

interpret the results taking other factors into consideration, such as psychological factors

would add even more value both from an analytical as well as from an organisational

perspective. Chapter 4 presents an attempt to collaborate psychology using Myer Briggs

Type Indicator (MBTI) into a context of employee engagement survey. The analytical

part has focused on the four types together with the 16 profiles following the MBTI and

- 163 -

the results indicate that we are able to find differences in impact structure following an

analysis of the EEI model based on each type/profile. The interpretation is that we do

find that there seems to be a possibility for differentiating employee preferences taken

psychological evaluation into consideration. However, this study was a trial within the

area of combining two sciences and the implications towards data quality are very much

assumed to bias the results, therefore further research should especially focus on i) make

use of more questions per type to be able follow a more dimensional approach as is the

case within MBTI ii) extend the research to a more global set-up to be able to capture

assumed cultural differences and iii) explore other means of psychological evaluations

in order to grasp differences and similarities between the different approaches at hand.

The author hopes that the contribution made here within the field of PLS,

structural equation modelling and the intra-related scope towards the field of

psychology has given both thoughts, curiosity and encouragement to continue the path

of pursuing research with the aim of closing more gaps, both from a theoretical as well

as from an empirical perspective.