Latent Variables, Constructs, and Constructions

1. Latent Variables, Constructs, and Constructions Bergen, August 2009 Roy Howell Texas Tech University

2. Latent Variables, Constructs, and Constructions First, some acknowledgements: Einar Breivik, whose questions made me change my thinking about the idea of formative measurement (after 20 years of being wrong) Sigurd Troye, who observed that science advances through the development of more complex theories about more precisely measured constructs

3. Denny Borsboom, who thinks (and writes) more clearly about the intersection of philosophy of science and psychometrics than anyone. • Bob McGrath, whose work gave me a vocabulary for discussing this topic.

4. 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

5. 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)

6. 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

7. Job 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

8. 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) • REPRESENTATIONAL ACCURACY???

9. 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.

10. 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.

11. 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 • 5. The quest for reliability

12. Social constructions and communication Complex constructs exist as social constructions – a lable 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

13. “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)

14. “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)”

15. Indexing • Pragmatic value of indexing • DJI, Index of leading indicators, etc. • Not taken as ‘constructs’

16. Categorization • The need for categorization • “Depressed” (clinical), “Insane”(forensics), “Mentally Disabled”(education, social services) • The “Diagnostic View” (Borsboom 2008) • Consistent with latent classes

17. 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 …

18. Degree of “construct” (you pick)? 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 and objective definition of necessary and sufficient conditions for placement on a construct” (McGrath 2005)

19. 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)

20. 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.

21. 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.

22. Complex constructs as causal systems B Panic attack Concern Worry Behavior Panic Disorder

23. Market Orientation Info gathering  Info Dissemination  Acting • SES Education  Occupation  Wealth  Housing

24. Reflective Brand Equity Multidimensional: Shared variance Shared and unique variance

25. Structural Model Perceived Quality Brand Loyalty Brand Equity Brand Awareness Brand Associations From Buil, de Chernatony, and Martinez, 2008 Thought Leaders Conference

26. 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?

27. 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 if have is age, I probabilistically infer it. Or, it might be that in a different research context my interest is in the maturation associated with age, or the cumulative experience gained over time as one ages, or perhaps with the cognitive effects of aging in a gerontology study, or with 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.

28. Take, for example, the relationship between observed age and performance on a given task in the adult population. It is not inconceivable that experience and judgment (positive latent outcomes of age) are positively related to task performance, while decreased physical and cognitive capacity (again latent outcomes positively related to age) may relate negatively to task performance. If these latent outcomes of age happen to cancel each other out, how does one interpret the finding that age is not related to task performance?

29. “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 latent variables.

30. Income, Race, Education, etc. ? • What is the referent of observed variables in a given research context? • In summary, my interpretation of observables is that they should be considered latent, multidimensional variables imperfectly and often non-linearly related to their multiple latent dimensions, and that only a subset of the dimensions of the observed variable are of interest in a given research context. They should be explicitly treated as such until, following Borsboom, proven otherwise. There is ‘surplus meaning’ (perhaps in a different sense than Cronbach and Meehl, 1955) and indeed, as Borsboom suggests, observed variables are ‘considerably more mysterious than commonly supposed.’

31. What to Do? • Conceptualize and measure at the elemental level • Model at the elemental level • “Vector Variables” (Econometrics) • “Multivariate Regression” (Edwards 2001)

32. Extraversion Dimensions Response to ConflictAssertivenessActivity Avoidance -.59* .04 Resolution .30* .28 Control 1.27* -.76* Other extraversion dimensions: Warmth, Gregariousness, Excitement seeking, Positive Emotions From Edwards (2001)

33. Job Satisfaction  Adaptation R2=.04 (N=348) Dimensions Work Coworkers Pay R2 Unfavorable job behaviors .12* -.09 .04 .04 Lateness -.76 .10 -.16* .10 Absenteeism -.06 .03 -.03 .08 Turnover Intent -.22* -.17* -.05 .22 Desire to Retire -.32* -.09 .10* .14 Abbreviated from Edwards (2001)

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

35. 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)

36. 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.

37. 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.

38. 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.”

39. 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

40. Partial References Borsboom, 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 Assessment, 85, 112-124.