Factor analysis of variables with 2, 3, 5, and 7 response categories: A comparison of categorical variable estimators using simulated data

Two estimators in the factor analysis of categorical items are studied, the weighted least squares function implemented in the tandem PRELIS-LISREL 7 and a generalized least squares function implemented in LISCOMP. Of main interest is the performance of these estimators in relatively small samples (200 to 400) and the comparison of their performance with the normal theory maximum likelihood estimator given an increasing number of response categories. The evaluation of the performance of these estimators concerns the variability of the parameter estimates, the bias of the parameter estimates, the distribution of the parameter estimates and the χ2 goodness-of-fit statistics. The model used in the simulation is an 8-indicator single common factor model. The effect of model size (12- and 16-indicator models) on the categorical item estimator of LISREL 7 is investigated briefly. The results indicate that in the ideal circumstances of the simulation study, 200 is too small a sample size to justify the use of large sample statistics associated with these estimators.