1. Factor Analysis Ulf H. Olsson Professor of Statistics

2. Ulf H. Olsson ML and GLS are asymptotically equivalent If The models holds in the population The observed variables are multivariate normal

3. Ulf H. Olsson Large-sample properties

4. Ulf H. Olsson CFA example NPV-data set Chi-square tests Modification indices T (Z)-values Df ∆chi-square tests

5. Ulf H. Olsson The Wald Test

6. Ulf H. Olsson Example of the Wald test Consider a simple regression model

7. Ulf H. Olsson General Fit Function

8. Ulf H. Olsson Making Numbers

9. Ulf H. Olsson Making Numbers

10. Ulf H. Olsson Making Numbers

11. Ulf H. Olsson Making Numbers

12. Ulf H. Olsson Two ML functions C1 and C2 k is the number of manifest variables. D is the duplication matrix (Magnus and Neudecker 1988) and is the ML estimate.

13. Ulf H. Olsson C3 and C4 Satorra & Bentler, 1988, equation 4.1

14. Ulf H. Olsson ESTIMATORS If the data are continuous and approximately follow a multivariate Normal distribution, then the Method of Maximum Likelihood is recommended. If the data are continuous and approximately do not follow a multivariate Normal distribution and the sample size is not large, then the Robust Maximum Likelihood Method is recommended. This method will require an estimate of the asymptotic covariance matrix of the sample variances and covariances.