Structural Equation Modeling

1. Structural Equation Modeling Mgmt 291 Lecture 4 Model Specification & Data Preparation Oct. 19, 2009

2. What we have:1) National Level Research • Government capability (Governance) • Corruption – Political Instability – Property Right – Rule Regulation • Foreign Direct Investment • Data – need to merger datasets ? Shanshan Qiu

3. 2) Firm Level Research • 1) Earning • Stock price • ??? • 2) Football team Abilities => Score Points John Bae Matthew Feldmann

4. 3) Individual Level Research • 1) Why starting a business Interests - Belief => Starting • 2) Consuming a green product Wealth Value => Organic Food Consumption Life-style Laura Huang Hannah Oh 3) Analysts behavior by Joshua

5. A few issues on first assignment: 1) Theory -> Operationalization need to be completed • Theory & Concepts • -> Data & Variables • Questions -> Hypotheses • Concepts and Variables linked

6. 2) Confirmative Approach vs. Exploratory Approach need to be clear • Clear Theory-backed hypotheses • Strictly confirmative ? • (maybe some exploratory elements added later are fine) • Usually start with confirmative if theories are strong. • OR completely exploratory.

7. 3) Clear Strategies Needed • Extend • Replicate previous research • Test some theories empirically • Review literature – some critique – are necessary. • (need to know how important your research is, what your contribution is)

8. 4) Need SEM Type of Questions (that can NOT be handled by OLS regression) • Mediation effects • Latent Variables • Non-recursive • Correlated Disturbances (Errors or Residuals) • - model comparison (15 fit indexes) SEM Types of Hypotheses

9. Or Causality Questions • Time precedence ? • Direction – (need SEM to rule out other direction) • Partialed out • (panel studies, • disturbance – non-deterministic)

10. Or Group Comparison Questions • Measurement Invariance Cross Groups • Structure Invariance Cross Groups

11. Example of Literature Review • Literature review – a lot of research on determinants of economic growth AND determinants of democracy, a few article starting to argue that DEMOCRACY needs to be treated as latent var. • Lack of empirical study of the feedback loop of economic growth and democracy. • Indirect impacts of determinants are rare.

12. Example of SEM Questions • Democracy is a latent variable with Freedom House indicator, Polity indicator, Polyarchy Indicator and others (FH, ACLP in our data) • democracy and economic growth may be affected by each other. • The impacts of economic development on democracy may be indirect.

13. Example of data and variables • D&D Data Description • A table to list • all the variables. • See • http://www.researchmethods.org/sem-data.htm • for the data and codebook.

14. For Second Assignment move to model specification • Hypotheses or theories <-> model (to be represented by diagrams)

15. Hypotheses or Model Spec Generation • Exploratory way • use partial correlation • to generate model spec

16. An Algorithm • 1) Link all vars together • 2) Take out links corresponding to in sig partial correlations • Repeat 1-2 to take out as many as possible • 3) use theory or common sense to place directions • 4) use partial correlation to place more directions • Repeat 3-4 to change all un-directional links to directed links

17. Specification Issues • Avoid Misspecification • External (missed variables) • Internal (missed links) • Sufficient number of indicators for each latent variable (2 is fine, 3 is better, 4 is the best, …) • Do Your Best to Specify Directions • Parsimony - Important

18. Misspecification Problems -> Biases Over-estimation Suppression (depends on the correlation between vars in the equation and vars omitted

19. Another Model Specification Issue – interaction terms Z1 • Moderated effects Z2 e1 Y1 e2 X1 Z3 Y2 Z4 X2 Z5 e3 4 more matrix X1*X2 Y3 Z6 Z7

20. Model Specification Example Econ FH Polity ACLP Polyarchy Openc Democracy Edu Gini Bricol ELF60 Riots ODRP Error terms needed

21. 2 Step Approach for Model Identification Measurement Model Econ FH Polity ACLP Polyarchy e Democracy Openc Edu Democracy Structure Model Gini Bricol ELF60 Riots ODRP 2 Step Approach

22. Model Identification 2-step Example Measurement Model Econ FH Polity ACLP Polyarchy e Democracy Openc Edu Democracy Structure Model Gini Bricol ELF60 Riots ODRP 2 Step Approach

23. Data Preparation • Missing Values • Normality • Multicollinearity • Linearity

24. Missing Values Edt & Gini significant • Statistics • BRITCOL8 ELF80 LEVEL80 ODRP80 RIOTS80 CCODE80 CIVLIB90 POLLIB90 REG90 • Missing 7 7 7 • 7 7 7 • 23 23 23 Pairwise Listwise

25. Normality

26. Multicollinearity >.90 results 1s or Os Making matrix calculation impossible Corr > .85 Tolerance (1-R2) < .10 VIF (1/ 1-R2) > 10

27. Linearity

28. Outliers • outliers can distort the results greatly

29. Variable Transformation • Power Function • Log For normality, linearity,

30. Start Thinking about programming • Β - betaη - etaξ - xiζ - zetaΓ - gammaΛ - lambda (upper case)λ - lambda (lower case)δ - deltaε - epsilon NY NX NK NE

31. Introducing R • R is FREE at www.r-project.org • R is very popular and powerful (see the NY Times article) • SEM in R example

32. > sem1 <- matrix(c( • + + 1.0, 0, 0, 0, 0, • + + .516, 1.0, 0, 0, 0, • + + .453, .438, 1.0, 0, 0, • + + .332, .417, .538, 1.0, 0, • + + .322, .405, .596, .541, 1.0), • + + 5, 5, byrow=TRUE) • > rownames(sem1) <- colnames(sem1) <- c("FatherEd", "FatherOcc", "Education", "FirstJob", "1962Job") • > library(sem) • > model.sem1 <- specify.model() • FatherEd -> Education, gamma31, NA • FatherOcc -> Education, gamma32, NA • FatherOcc -> FirstJob, gamma42, NA • Education -> FirstJob, beta43, NA • FatherOcc -> 1962Job, gamma52, NA • Education -> 1962Job, beta53, NA • FirstJob -> 1962Job, beta54, NA • Education <-> Education, sigma66, NA • FirstJob <-> FirstJob, sigma77, NA • 1962Job <-> 1962Job, sigma88, NA • > sem.1 <- sem(model.sem1, sem1, 20700 , fixed.x=c("FatherEd", "FatherOcc")) • > summary(sem.1) • > path.diagram(sem.1)

33. About the Assignment • Modify your hypotheses • 1) Specify a few SEM models • 2) Check their identification issues • 3) Prepare your data • Write a 2 page report