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 Alternative test- Testing Close fit

7. 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

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

9. Ulf H. Olsson Nine Psychological Tests

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

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

12. Ulf H. Olsson Alternative Estimators

13. Ulf H. Olsson Alternative Estimators

14. Ulf H. Olsson Alternative Estimators