1. GRA 6020 Multivariate Statistics Confirmatory Factor Analysis Ulf H. Olsson Professor of Statistics

2. Ulf H. Olsson CFA The covariance matrices:

3. Ulf H. Olsson CFA and ML k is the number of manifest variables. If the observed variables comes from a multivariate normal distribution, then

4. Ulf H. Olsson Testing Fit

5. Ulf H. Olsson Problems with the chi-square test The chi-square tends to be large in large samples if the model does not hold It is based on the assumption that the model holds in the population It is assumed that the observed variables comes from a multivariate normal distribution => The chi-square test might be to strict, since it is based on unreasonable assumptions?!

6. Ulf H. Olsson Univariate Normal Distribution

7. Ulf H. Olsson Bivariate normal distribution

8. Ulf H. Olsson J-te order Moments Skewness Kurtosis

9. Ulf H. Olsson Kurtosis

10. Ulf H. Olsson Standard Normal density functions

11. Ulf H. Olsson Alternative test- Testing Close fit

12. Ulf H. Olsson How to Use RMSEA Use the 90% Confidence interval for EA Use The P-value for EA RMSEA as a descriptive Measure RMSEA< 0.05 Good Fit 0.05 < RMSEA < 0.08 Acceptable Fit RMSEA > 0.10 Not Acceptable Fit

13. Ulf H. Olsson Other Fit Indices CN RMR GFI AGFI Evaluation of Reliability MI: Modification Indices

14. Ulf H. Olsson Nine Psychological Tests

15. Ulf H. Olsson Alternative Estimators Assuming multivariate normality ML GLS ULS If the model holds, ML and GLS are asymptotically equivalente

16. Ulf H. Olsson Alternative Estimators S: sample covariance θ: parameter vector σ(θ): model implied covariance

17. Ulf H. Olsson Alternative Estimators

18. Ulf H. Olsson Alternative Estimators

19. Ulf H. Olsson Alternative Estimators

20. Ulf H. Olsson Assignment 1 The Country/People Image 12 items was used for the country-people Image: For each item a 7-point semantic differential scale was used 1) Role in world politics 2) Refined taste 3) Likable 4) Trustworthy 5) Industrious 6) Managing the economy well 7) Technological level 8) Ability to handle large and complex projects 9) Would like closer ties 10) Educational level 11) Polluted environment 12) Athletic People Research project: Use the file CI-week11.psf to find a factor structure for the Construct Country Image. Test and evaluate the model.

21. Ulf H. Olsson Assignment 2 Political Efficacy Campel et al. (1954): Political Efficacy is the feeling that individual political action does have, or can have, an impact upon political process. Observed (measured) variables: NOSAY: People like me have “no say” in what the government does VOTING: Voting is the only way that people like me can have “any say” about how the government runs things. COMPLEX: Sometimes politics and government seem so complicated that a person like me cannot really understand what is going on NOCARE: I don’t think that public officials care much about what people like me think TOUCH: Generally speaking, those we elect to Parliament lose touch with people pretty quickly INTEREST: Parties are only interested in people’s votes but not in their opinions Use the data set in the file: Efficacy2005.psf and find a suitable factor model