GRA 6020 Multivariate Statistics Confirmatory Factor Analysis

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

2. CFA • The covariance matrices: Ulf H. Olsson

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

4. Testing Fit Ulf H. Olsson

5. 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?! Ulf H. Olsson

6. Univariate Normal Distribution Ulf H. Olsson

7. Bivariate normal distribution Ulf H. Olsson

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

9. Kurtosis Ulf H. Olsson

10. Standard Normal density functions Ulf H. Olsson

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

12. 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 Ulf H. Olsson

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

14. Nine Psychological Tests Ulf H. Olsson

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

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

17. Alternative Estimators Ulf H. Olsson

18. Alternative Estimators Ulf H. Olsson

19. Alternative Estimators Ulf H. Olsson

20. 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.   Ulf H. Olsson

21. 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 Ulf H. Olsson