Latent Variables, Constructs, and Constructions

Roy HowellTexas Tech University

Latent Variables, Constructs, and Constructions

• Premise: It takes both conceptual clarity and representational accuracy to advance the process of knowledge accumulation.

• Many constructs in the social sciences are conceptually complex.

• This often leads to complex measures that lack representational accuracy (validity)– Representational accuracy is fundamental to model

building

Conceptual Complexity

• “Conceptual Complexity refers to the degree to which the construct [hierarchically] encompasses conceptually distinct subconstructs” (McGrath 2005, brackets added)– Often referred to as “multidimensional constructs”

in the management and OB literature (Law, Wong & Mobley, AMR 1998; Edwards 2001)

Just a few (of many) examples

• Socioeconomic status (SES)– Income, education, occupation, housing.

• The ‘Big 5’ personality traits are all conceptually complex – Openness, Conscientiousness, Extraversion, Agreeableness, Neuroticism

• For example, Extraversion refers to– Warmth, Gregariousness, Assertiveness, Activity, Excitement Seeking,

Positive Emotions– Each of these conceptually distinct subconstructs has subdimensions, too– A person can be warm without being active, or assertive without positive

emotions

• Consumer Confidence Index1. How does the financial situation of your household’s now compare with what it was 12 months ago?2. How do you think the financial position of your household’s will change over the next 12 months?3. How do you think the general economic situation has changed over the last 12 months? 4. How do you think the general economic situation will develop over the next 12 months? 5. Do you think there are benefits in people making major purchases such as furniture, washing

machines, TV sets at the present time?The responses to questions 1–4 are weighted: (a) a lot better (+1); (b) a little better (+0.5);(c) the same (0);(d) a little worse (−0.5);(e) a lot

worse (−1). Responses to question 5 is coded (a) yes, now is the right time (+1); (b) neither right nor wrong time (0); (c) no, wrong time, purchases should be postponed (−1).

• Satisfaction– Pay, Coworkers, Supervisor, Job Itself, etc.– Pay: input/output, equity, etc.– Job: autonomy, feedback, authority, etc.

• Market Orientation– Information Collection, Information Dissemination, Acting on Information

• Diagnostic Classifications are just as bad, or worse– Depression – behavioral, emotional, cognitive, and physiological dimensions

How do we measure complex constructs?

• Simple Aggregation (sum score)• Factor Analysis (first or second order)

accounting for covariance among subconstructs

• Formative Measurement (weighted composite) – extreme form of a multidimensional construct

• REPRESENTATIONAL ACCURACY???

Why It Matters

Studies that have compared scales (whether aggregate or higher-order factors or formative measurement) composed of conceptually distinct constructs at different levels of complexity have consistently found that both prediction and understanding are enhanced by using a larger number of specific variables rather than a smaller number of more global ones.

Some of the studies

• Mershon & Gorsuch, JPSP 1988; Paunonen, JPSP 1998; Schneider et al. JPSP 1996 (Title—”Broadsided by Broad Personality Traits: How to sink science in five dimensions or less”); Edwards, ORM 2001; Howell et al. 2007; McGrath 2005.

WHY DOES IT HAPPEN?

• 1. Social constructions and communication• 2. Pragmatic value of Indexing• 3. The need for categorization in application• 4. Predisposition to organize the world

according to prototypes & Radial categories• 5. The quest for reliability

Social constructions and communication

Complex constructs exist as social constructions – a label used to summarize a loosely bounded set of observed regularities (Gergen 1985, Amer. Psychologist)

“flexible verbal summaries”“a socially useful label”Reduce information load for the purposes of

comprehending information and communicating it to others

• “The belief that a person can be characterized in terms of a few global concepts such as depression, intelligence, or responsibility is a seductive one, as it is both easier to grasp and easier to communicate to others than a larger set of more specific constructs” (McGrath 2005)

• “However, when one gives a name to a collection of attributes or characteristics in a common realm for the sake of convenient communication and then treats them as if the corresponding entity exists, ‘one is reifying terms that have no other function than that of providing a descriptive summary of a set of distinct attributes and processes (Borsboom et al. 2004)’ (Howell et al. 2007)”

Indexing

• Pragmatic value of indexing– Index of Consumer Sentiment; DJI; Index of

Leading Indicators, etc.• Not taken as ‘constructs’

Categorization

• The need for categorization– “Depressed” (clinical), “Insane”(forensics),

“Mentally Disabled”(education, social services)• The “Diagnostic View” (Borsboom 2008)– Consistent with latent classes

Prototypes

• Natural predisposition to organize the world according to prototypes:– “Joe is an extrovert”

• Loud, active, fun-loving, outgoing• Some definitional, others correlates – and can be active and fun

loving but not loud– Exemplar extrovert – all of the above– Exemplar Depressive – sad, hopeless, suicidal thoughts,

negative emotionality, no pleasure• Exemplar Organizational Citizen, Market Oriented Firm,

Upper class family …

• Degree of “the construct”? Few cases are exemplars, however. For most there are varying degrees of distance from the prototype ON MULTIPLE DIMENSIONS.

• “The ability to define a prototype does not substitute for the scientific process of deriving an objective definition of necessary and sufficient conditions for placement on a construct” (McGrath 2005)

• Radial Categories– Categorized by variations on a central model• Mother : birth, genetic, nurturance, marriage• Central tendencies and variations• The category extends to cases where only some of the

conditions are met

The Quest for Reliability

• More items increase reliability, given correlations

• Reliability is not unidimensionality or conceptual consistency

• Items representing correlated but distinct constructs can generate adequate reliability with enough items (but redundancy between items does not imply high correlation – the difficulty factor)

But if there is correlation among conceptually distinct constructs, where does it come from?

• Response or single source bias. Because a single respondent fills out an entire questionnaire, there is a risk that systematic variance unrelated to the constructs themselves will be present among otherwise unrelated items (Podsakoff and Organ, 1986).

• Artifact. Given the common use of integer rating scales, floor or ceiling effects can lead to spurious correlation among items.

• Halo. When one attribute is used to generalize about other attributes of the same object, even though the attributes are unrelated, it is referred to as halo effect (Fisicaro & Lance, 1990). Whether halo is attributable to cognitive bias or cognitive laziness, the result is correlation among the traits.

Sources of Correlation• Structural. A “measurement” model may indeed be a structural

model (Borsboom 2008). To the extent that structural relationships are strong, the items may be correlated, but this is not due to the common cause of a latent variable or underlying construct.

Complex constructs as causal systems

BPanic attack

Concern Worry Behavior

Panic Disorder

• Market OrientationInfo gathering Info Dissemination Acting

• SES Education Occupation Wealth Housing

Reflective Brand Equity

Multidimensional:

Shared variance

Shared and unique variance

Structural Model

Brand Awareness

Perceived Quality

Brand Associations

Brand Loyalty Brand Equity

From Buil, de Chernatony, and Martinez, 2008 Thought Leaders Conference

Can an “observed variable” be complex or multidimensional?

• Sex -- just a y-chromosome? Only for a biologist.

• Age – just number of years since birth?As in differences in chromosomes, age as the

duration of time since a person’s birth is indeed measurable, but when is that really of interest?

• If the study is in developmental psychology from the perspective of, say, Piaget, then my interest is in developmental periods that are roughly dependent on age. I would of course like to have measured the (latent) developmental period directly, but if all I have is age, I probabilistically infer it.

• In different research contexts:– the maturation associated with age, – the cumulative experience gained over time as one ages,– the cognitive effects of aging in a gerontology study, – the physical effects of aging, – or generational or cohort effects associated with age, or economic effects

of aging (income effects, consumption differences). The list of probabilistic outcomes of age goes on.

“Observed” Variables?

Observed variables are seldom of interest in and of themselves, and are usually in practice used as imperfect surrogates for their unobserved outcomes, which can be numerous. In a data structure the analyst has a column of numbers designated as ‘age’ but, depending on the research context, is theorizing about one or a subset of its many outcomes. When using age as a variable, however, the researcher gets the whole thing, not just the outcomes of interest in that instance. That is, I believe that many observed variables are inherently multidimensional or complex latent variables.

• Income, Race, Education, etc. ?• What is the referent of observed variables in a

given research context?

What to Do?

• Conceptualize and measure at the elemental level

• Model at the elemental level• “Vector Variables” (Econometrics)• “Multivariate Regression” (Edwards 2001)

Extraversion DimensionsResponse toConflict Assertiveness ActivityAvoidance -.59* .04Resolution .30* .28Control .27* -.76*

Other extraversion dimensions: Warmth, Gregariousness, Excitement seeking, Positive Emotions

From Edwards (2001)

Job Satisfaction Adaptation R2=.04 (N=348)

Dimensions Work Coworkers Pay R2 Unfavorable job behaviors .12* -.09 .04 .04Lateness -.76* .10 -.16* .10Absenteeism -.06 .03 -.03 .08Turnover Intent -.22* -.17* -.05 .22Desire to Retire -.32* -.09 .10* .14

Abbreviated from Edwards (2001)

• Communication can be facilitated by calling the dimensions “SES Variables” or “Job Satisfaction Variables”, for example, to describe their common domain.

What if we do this?

• That is, what if we reduce the conceptual complexity of our constructs?

• Better, if more complex theory• “From lean theory and ‘rich’ constructs to rich

theory and lean constructs” (Troye, 1996, OAB)

Perceived Risk

• Bauer (1960), Cox (1961), Cox & Rich (1964)• “How much would you worry about buying this item?”• Engle 1968 – “Risk is a complex concept, and these

complexities are largely ignored. As it has been used, risk is an umbrella term that covers many underlying variables… “

• Roselius (1971) – Time loss, hazard loss, ego loss, money loss

• (1980’s) Physical, Financial, Social, Performance, with risk reduction strategies that differ for each.

Other Examples

• Fishbein A(j)• Extended Fishbein A(act), SNB, MC• Theory of Trying (Bagozzi) 12 constructs

• Edwards (2001) “As constructs in the OB field are refined, distinctions that were previously overlooked often became clear and compelling -- Job characteristics, Job stress, Organizational Commitment – each of which has drawn progressively finer distinctions within constructs once treated as unidimensional.

• Edwards, cont.As constructs become more differentiated,

information specific to construct dimensions becomes increasingly relevant, and multidimensional construct models become less useful than multivariate structural models that treat construct dimensions as a set.”

Issues

• Reductionism – can we go too far in ‘distinguishing’?

• Necessary & sufficient conditions. • Cognitive Diagnostic Models -- Conjunctive

“and”, disjunctive “or”, compensatory• Intra-individual level theories and structure

Partial ReferencesBorsboom, D. (2008) . Latent Variable Theory. Measurement, 6(1-2), 25-53.Borsboom, D. (2005). Measuring the mind: Conceptual issues in contemporary psychometrics.

Cambridge University Press.Borsboom D, Mellenbergh GJ, van Heerden J. The theoretical status of latent variables. Psychol

Rev 2003;110:203-19.Borsboom D, Mellenbergh GJ, van Heerden J. The concept of validity. Psychol Rev 2004;111:1061-

71.Cronbach, L. J. & Meehl, P. E. (1955). Construct Validity in psychological tests. Psychological

Bulletin, 52, 281-302.Edwards, J. R. (2001). Multidimensional constructs in organizational behavior research: An

integrative analytic framework. Organizational Research Methods, 4, 144-192.Howell, R.D. (2008). Observed Variables are Indeed More Mysterious than Commonly Supposed.

Measurement, 6(1-2), 97-100.Howell, R. D., Breivik, E., & Wilcox, J. B. (2007). Reconsidering formative measurement.

Psychological Methods, 12, 205-218.Howell, R. D., Breivik, E., & Wilcox, J. B. (2007). Is Formative Measurement Really Measurement?

Psychological Methods, 12, 238-245.McGrath, R.E. (2009). On Prototypes and Paradigm Shifts. Measurement, 7(1), 27-29.McGrath, R.E. (2005). Conceptual Complexity and Construct Validity. Journal of Personality

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