Factor Analysis Ulf H. Olsson Professor of Statistics

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

Ulf H. Olsson Large-sample properties

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

Ulf H. Olsson The Wald Test

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

Ulf H. Olsson General Fit Function

Ulf H. Olsson Making Numbers

Ulf H. Olsson Making Numbers

Ulf H. Olsson Making Numbers

Ulf H. Olsson Making Numbers

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.

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

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.