Different chi-squares Ulf H. Olsson Professor of Statistics

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 Ordinal Variables In practice, observed or measured variables are often ordinal However, ordinality is often ignored and numbers such as 1,2,3, etc. representing ordered categories, are treated as continuous variables. But, this is incorrect! READ ch. 2.1 (Jøreskog April 2002)

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. If the data are ordinal, categorical or mixed, then the Diagonally Weighted Least Squares (DWLS) method for Polychoric correlation matrices is recommended. This method will require an estimate of the asymptotic covariance matrix of the sample correlations.

Ulf H. Olsson RMSEA

Ulf H. Olsson RMSEA