MKT 8543 Quantitative Marketing Seminar

1. MKT 8543 Quantitative Marketing Seminar • Today’s Topics: • The SEM Process • Theory/Measurement Interaction and • Reflective versus Formative Indicators • January 20, 2009 Mississippi State University Nicole Ponder

2. The Logic of SEM (Kelloway Chapter 2) Subjective Norms • Fishbein and Ajzen’s (1975) theory of reasoned action • This theory is an explanation of how these constructs are correlated (or not correlated), as every theory implies a set of correlations • If the theory is valid, then the theory should be able to explain or reproduce the patterns of correlations in the data Behavioral Intentions Beliefs Attitudes Behavior

3. The SEM Process (Kelloway Chapter 2) • Model specification • Model identification • Estimation • Testing fit • Model respecification, or modification • And step 6, from Chin, Peterson, and Brown (2008); reporting the information correctly

4. Step 1: Model Specification • SEM is used for confirmatory purposes – it is not an exploratory tool • The purpose of your model is to explain why constructs are correlated in a particular way • What you are testing: Σdata = Σmodel

5. Model Specification Subjective Norms • “A model is a set of theoretical propositions that link the exogeneous variables to the endogeneous variables and the endogeoneous variables to one another. As a whole, the model explains both what relationships we expect to see in the data and what relationships we do not expect to emerge.” (K p. 8) Behavioral Intentions Beliefs Attitudes Behavior

6. Model Specification • A path diagram illustrates our model; all proposed causal relationships are assumed to be linear; all relationships are present in the model (absence of paths just as important as the presence of paths); all relationships are theoretically justified X Q Z Y

7. Step 2: Model Identification • Can a unique solution for the model be obtained? Or, am I able to estimate all of the parameters that need to be estimated in my model? • A just-identified model occurs when you provide the exact same number of elements in the covariance matrix as the number of parameters you are asking LISREL to estimate • An under-identified model means that you are asking LISREL to estimate more parameters than the number of covariances in your input matrix • What you want is an over-identified model, meaning that the number of equations exceeds the number of unknowns • SEM searches for the best solution that fits Σdata = Σmodel

8. Steps 3 & 4: Model Estimation & Fit • SEM searches for the best solution that fits Σdata = Σmodel • Most common/popular fitting function is maximum likelihood (ML), OLS and GLS also used (K p. 18) • Something you might say in a manuscript: “Data were analyzed with LISREL 8 using the covariance matrix as the input matrix and the maximum likelihood estimation method.” • Covariance matrix versus correlation matrix • Use of a correlation matrix when examining a measurement model can provide useful information • Most often, a covariance matrix is preferred; retains the original scale msmt. Units • What is an appropriate sample size?

9. Step 5: Model Respecification • “Alchemy,” “voodoo statistics,” because this occurs post hoc rather than a priori • In other words, this stage is more exploratory in nature, rather than confirmatory • Collect more data, employ the hold-out sample strategy • IF you relax model constraints to achieve a better fit, do so with caution! Remember the words of Bagozzi (1983) and Fornell (1983) • Always indicate when you have relaxed a constraint post hoc, and have a theoretical justification as to why that path was allowed in the model. • Test you respecified model on new data

10. Step 6: Clear & Informative Reporting What should be reported in an SEM-related manuscript: (Chin, Peterson, and Brown 2008) • The covariance matrix used, along with the sample size • The model setup, which parameters are fixed and freed, and start values if applicable • The software package used; the estimation method used • The discrepancy that exists between the model and the data • The chi-square and degrees of freedom for each model tested

11. Theory-Measurement Interaction • Theory defined: an invention aimed at organizing and explaining specific aspects of our environment • A theory can be thought of as an explanation of why variables are correlated (or not correlated); typically involves the development of hypotheses about causal relations (Kelloway 1998) • How is theory related to measurement? • Theory Construct definitions Measures

12. Theory-Measurement Interaction: Why Definitions are so Important! Theory Construct definitions Measures • Without well-developed construct definitions, it is impossible to develop a coherent theory because constructs are the building blocks of theory (MacKenzie 2003) • One cannot develop a meaningful theoretical rationale for why Construct A should be related to Construct B if the exact meaning of these two constructs have not been established (MacKenzie 2003)

13. Pointers for Developing Good Definitions • MacKenzie (2003) states that good definitions: • Specify the construct’s overriding conceptual theme • Are unambiguous • Are consistent with prior research on the concept • Clearly distinguish the construct from related constructs • Common mistakes to avoid: • Do not define a construct solely in terms of its antecedents and consequences (p. 325) • Do not define a construct only by providing examples of what the construct includes; need to specify the underlying theme that ties the exemplars together

14. Theory-Measurement Interaction • A theory can be thought of as an explanation of why variables are correlated (or not correlated)… (Kelloway 1998) • Basis for SEM: every theory implies a set of correlations, and if the theory is valid, then the theory should be able to explain or reproduce the patterns of correlations found in the empirical data • SEM tests whether Σmodel = Σdata, So theory and measures are closely related in SEM

15. Points from Fornell (1983) • Objective of SEM is to reproduce the observed covariance matrix as closely as possible and to determine how well the model fits the data • Overall chi-square statistic tests for overall model fit - does Σmodel = Σdata? • With SEM, you are looking for a non-significant chi-square; this goes against conventional hypothesis-testing wisdom • Any one of a number of theoretical models could fit the data equally well. This is why covariance structure analysis should be guided by substantive theory – otherwise, it is impossible to sort out competing empirical models (p. 445)

16. Points from Fornell (1983) • Idea of trivial fits: if you relax enough constraints, sure you’ll get a great fit, but you are not really predicting anything • “...almost any covariance matrix can be perfectly reproduced…when enough orthogonality constraints are dropped” (p. 444) • It is the restrictions or constraints (the absence of paths) that give the model its power • Does not like the notion that one might rely only on the chi-square to determine if the model fits the data…p. 446

17. Points from Fornell (1983) and Bagozzi (1983) • Its easy to get a non-significant chi-square, if you relax enough constraints • “Correlated measurement errors” means that something else is going on between these measures that is not being accounted for by the original model • Correlated measurement residuals imply that one or more omitted variables exist causing common variation in the measurements whose residuals covary • “Correlated measurement residuals are fall-back options that nearly always detract from the theoretical elegance and empirical interpretability of a study” (Bagozzi 1983, p. 450)

18. Other Points from Bagozzi (1983) • While SEM does allow for the simultaneous assessment of measurement and theory, it is often meaningful and useful to examine measurement models independent of the entire theoretical structure in which they are imbedded (p. 449) • Examine measurement model first in order to establish evidence of construct validity; then examine the structural model to establish predictive validity • Referred to as the two-step approach to model estimation

19. Important Point About Scales • Each item is intended to capture the entire definition of the construct • In other words, each item should be reflective of the entire construct of interest! • What each item in a scale have in common….that commonness defines the latent construct; the construct IS the commonness (commonality) of the indicators • Thinking about the relationship of the items to the construct in this way is very helpful! • What do quality of work life, quality of home life, and quality of extracurricular activities have in common?

20. Bollen and Lennox (1991) • Straightforward article that explains the difference between formative and reflective indicators • Refer to Figures 1a and 1b…if you understand this, SEM is soooo much easier! Understanding this, and only using reflective indicators in structural equation models helps A TON!

21. Bollen and Lennox (1991) • Figure 1a: the reflective (effects) model • Reflective measures are determined by the construct • The reflection is imperfect – there is also error representing systematic and random sources of variance • EFA and CFA are used for reflective measurement models  Y1 Y2 Y3 Y4 1 2 3 4

22. Bollen and Lennox (1991) • Figure 1b: the formative (cause) model • Formative measures determine or cause the construct • Examples: • SES=f(education, income, occupation, neighborhood) • Faculty performance=f(teaching, research, service) • Life satisfaction=f(work satisfaction, home satisfaction, extracurricular activities satisfaction) • You have formative measures if a change in the indicator causes a change in the construct (MacKenzie 2003, p. 325)  X1 X2 X3 X4

23. Five Important Points from Bollen and Lennox (1991) about Formative and Reflective Indicators • Point 1: Internal consistency (p. 307) • For the reflective model…those indicators that are measuring the same concept should be highly correlated amongst themselves • Coefficient alpha: how we test for internal consistency • For formative indicators (or causal indicators), we do not really know the correlations that exist between the indicators • Could be high and positive, but not necessarily • Consider SES and faculty performance, for example • Do NOT use Cronbach’s alpha on formative measures! (MacKenzie 2003, p. 326)

24. Five Important Points Concerning Formative and Reflective Indicators • Point 2: Optimal magnitudes of correlations between items (p. 307) • B&L point out that much discrepancy exists in the literature over how correlated your indicators should be • For reflective (effects) indicators, you want the correlations between them as high as possible! • For formative (causal) indicators, we are unsure about the optimal correlations. They could be highly related, but they certainly don’t have to be.

25. Five Important Points Concerning Formative and Reflective Indicators • Point 3: Sampling the domain and validity (p. 308) • Again, conflicting opinions about the items you select to represent a construct • B&L’s test: understand the consequences of removing indicators from your model • In Fig 1a – if you remove y4 from the model, what happens? • In Fig 1b, if you remove x4, what happens?

26. Five Important Points Concerning Formative and Reflective Indicators • Point 4: Within-construct correlations versus between-construct correlations (p. 308-09) • As a general rule of thumb, your within-construct correlations should be higher than your between-construct correlations • You want your items measuring the same construct to be related more highly than items measuring different constructs

27. Five Important Points Concerning Formative and Reflective Indicators • Point 5: If you create linear composites of your indicators, they should not be mistaken for the construct itself – still has error associated with it! (p. 309-10)

28. Next Week’s Class • Introduction to the measurement model • Parameters and equations associated with the measurement model • How to “set up” a measurement model in LISREL • Program syntax • Fixing and freeing parameters • Setting reference variables versus standardizing phi • Read Kelloway Chapter 4; re-read today’s readings in light of today’s discussion