ESTIMATION AND APPLICATION OF LATENT VARIABLE MODELS IN CATEGORICAL-DATA ANALYSIS

Bartholomew (1980, 1984a) has laid down a foundation for factor analysis based on latent variable models. Shea (1984, 1985) has provided computer programs for estimating one-factor latent variable models when responses are binary or polytomous variables. However, the programs have limitations on number of variables and the sample size, which limits their applicability, especially when variables are polytomous. However, the more important limitation is that it is not possible to use two-factor models when one-factor models are not adequate. Here, we have gone further and successfully obtained maximum likelihood estimates for both the one-factor and two-factor latent variable models for binary and polytomous variables. The new algorithm is much faster because of careful and efficient programming. More importantly, generalization to high latent domensions is straightforward. Formal hypothesis testing is very difficult when variables are very large in number. However, we have shown in our examples that some interesting graphical interpretations can be made.