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Chapter 19

Multivariate Analysis:

An Overview

McGraw-Hill/Irwin Copyri ght 2011 by The M cGraw-H il l Companies, Inc. All Rights Reserved.

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19-2

Learning Objectives

Understand . . .

How to classify and select multivariatetechniques.

That multiple regression predicts a metricdependent variable from a set of metricindependent variables.

That discriminant analysis classifies people orobjects into categorical groups using severalmetric predictors.

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19-3

Learning Objectives

Understand . . .

How multivariate analysis of variance assessesthe relationship between two or more metric

dependent variables and independentclassificatory variables.

How structural equation modeling explains

causality among constructs that cannot bedirectly measured.

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19-4

Learning Objectives

Understand . . .

How conjoint analysis assists researchers todiscover the most importance attributes and

the levels of desirable features. How principal components analysis extracts

uncorrelated factors from an initial set ofvariables and exploratory factor analysisreduces the number of variables to discoverthe underlying constructs.

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19-6

Wonder and Curiosity

Wonder, connected with a principle ofrational curiosity, is the source of allknowledge and discovery . . . but wonderwhich ends in wonder, and is satisfiedwith wonder, is the quality of an idiot.

Samuel Horsley

English scientist and fellow

Royal Society

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PulsePoint:

Research Revelation

60The percent of workers on four

continents who trust theirorganizations senior leaders.

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Classifying Multivariate

Techniques

InterdependencyDependency

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Multivariate Techniques

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Multivariate Techniques

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Multivariate Techniques

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Right Questions.

Trusted Insight.

When using sophisticated techniques

you want to rely on the knowledge of

the researcher.

Harris Interactive promises you can

trust their experienced research

professionals to draw the right

conclusions from the collected data.

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Dependency Techniques

Multiple Regression

Discriminant Analysis

MANOVA

Structural Equation Modeling (SEM)

Conjoint Analysis

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Uses of Multiple Regression

Develop

self-weightingestimating

equation to

predict values

for a DV

Control

forconfounding

Variables

Test

andexplain

causal

theories

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Generalized Regression

Equation

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Evaluating and Dealing with

Multicollinearity

Choose one of the variables

and delete the other

Create a new variable

that is a composite of the others

Coll ineari ty

Stat ist ics

VIF

1.000

2.289

2.289

2.748

3.025

3.067

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Discriminant Analysis

Predicted Success

Actual Group

Number of

Cases 0 1

Unsuccessful

Successful

0

1

15

15

1386.70%

320.00%

2

13.30%

12

80.00%

Note: Percent of grouped cases correctly classified: 83.33%

Unstandardized Standardized

X1

X1

X1

Constant

.36084

2.61192

.53028

12.89685

.65927

.57958

.97505

A.

B.

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19-20

MANOVA

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19-22

Bartletts Test

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MANOVA

Homogeneity-of-Variance

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Multivariate Tests of

Significance

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Univariate Tests of Significance

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Structural Equation

Modeling (SEM)

Model Specification

Estimation

Evaluation of Fit

Respecification of the Model

Interpretation and Communication

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Structural Equation

Modeling (SEM)

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Concept Cards for Conjoint

Sunglasses Study

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19-29

Conjoint Analysis

Brand Bo l le Hobbies Oakley Ski

Opt iks

Style* A

B

C

A

B

C

A A

Flotat ion Yes

No

Yes Yes Yes

Price $100

$72

$60$40

$100

$72

$60$40

$100

$72

$60$40

$100

$72

$60$40

* A = multiple color choices for frames, lenses, and temples.

B = multiple color choices for frames, lenses, and straps (no hard

temples.

C = limited colors for frames, lenses, and temples.

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Conjoint Results

Participant 8 in Sunglasses

Study

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Conjoint Results for

Sunglasses Study

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Interdependency Techniques

Factor Analysis

Cluster Analysis

Multidimensional Scaling

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Factor Analysis

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Factor Matrices

A

Unrotated Factors

B

Rotated Factors

Variab le I II h2 I II

AB

C

D

E

FEigenvalue

Percent of variance

Cumulative percent

0.700.60

0.60

0.50

0.60

0.602.18

36.3

36.3

-.40-.50

-.35

0.50

0.50

0.601.39

23.2

59.5

0.650.61

0.48

0.50

0.61

0.72

0.790.75

0.68

0.06

0.13

0.07

0.150.03

0.10

0.70

0.77

0.85

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19-37

Factor Matrix, Metro U

MBA Study

Variable Cour se Factor 1 Factor 2 Factor 3 Communali ty

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10Eigenvalue

Percent ofvariance

Cumulativepercent

Financial Accounting

Managerial Accounting

Finance

Marketing

Human Behavior

Organization Design

Production

Probability

Statistical Inference

Quantitative Analysis

0.41

0.01

0.89

-.60

0.02

-.43

-.11

0.25

-.43

0.251.83

18.30

18.30

0.71

0.53

-.17

0.21

-.24

-.09

-.58

0.25

0.43

0.041.52

15.20

33.50

0.23

-.16

0.37

0.30

-.22

-.36

-.03

-.31

0.50

0.350.95

9.50

43.00

0.73

0.31

0.95

0.49

0.11

0.32

0.35

0.22

0.62

0.19

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Varimax Rotated Factor Matrix

Variable Cou rse Factor 1 Factor 2 Factor 3

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

Financial Accounting

Managerial Accounting

Finance

Marketing

Human Behavior

Organization Design

Production

Probability

Statistical Inference

Quantitative Analysis

0.84

0.53

-.01

-.11

-.13

-.08

-.54

0.41

0.07

-.02

0.16

-.10

0.90

-.24

-.14

-.56

-.11

-.02

0.02

0.42

-.06

0.14

-.37

0.65

-.27

-.02

-.22

-.24

0.79

0.09

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Cluster Analysis

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Cluster Membership

________Number of Cluster s ________

Film Country Genre Case 5 4 3 2

Cyrano de Bergerac

Il y a des Jours

Nikita

Les Noces de Papier

Leningrad Cowboys . . .

Storia de Ragazzi . . .

Conte de Printemps

Tatie Danielle

Crimes and Misdem . . .

Driving Miss Daisy

La Voce della Luna

Che Hora E

Attache-Moi

White Hunter Black . . .

Music Box

Dead Poets Society

La Fille aux All . . .

Alexandrie, Encore . . .

Dreams

France

France

France

Canada

Finland

Italy

France

France

USA

USA

Italy

Italy

Spain

USA

USA

USA

Finland

Egypt

Japan

DramaCom

DramaCom

DramaCom

DramaCom

Comedy

Comedy

Comedy

Comedy

DramaCom

DramaCom

DramaCom

DramaCom

DramaCom

PsyDrama

PsyDrama

PsyDrama

PsyDrama

DramaCom

DramaCom

1

4

5

6

19

13

2

3

7

9

12

14

15

10

8

11

18

16

17

1

1

1

1

2

2

2

2

3

3

3

3

3

4

4

4

4

5

5

1

1

1

1

2

2

2

2

3

3

3

3

3

4

4

4

4

3

3

1

1

1

1

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

1

1

1

1

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

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Dendogram

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Similarities Matrix of 16

Restaurants

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Positioning of Selected

Restaurants

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Key Terms

Average linkage method

Backward elimination

Beta weights

Centroid

Cluster analysis

Collinearity

Communality

Confirmatory factoranalysis

Conjoint analysis

Dependency techniques

Discriminant analysis

Dummy variable

Eigenvalue Factor analysis

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Key Terms (cont.)

Factors

Forward selection

Holdout sample Interdependency

techniques

Loadings Metric measures

Multicollinearity

Multidimensionalscaling (MDS)

Multiple regression Multivariate analysis

Multivaria analysis of

variance (MANOVA) Nonmetric measures

Path analysis

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Key Terms (cont.)

Path diagram

Principal components

analysis Rotation

Specification error

Standardizedcoefficients

Stepwise selection

Stress index

Structural equationmodeling

Utility score