Latent variable models for categorical data

Abstract

In the previous two chapters it has been implicitly assumed that the observed variables represent measurements which are, at least approximately, on an interval scale. In addition, attention has been focused on maximum likelihood estimation assuming that the variables have a multivariate normal distribution, although the procedure may still lead to satisfactory parameter estimates if the data are moderately non-normal. However, in many research studies undertaken in the social and behavioural sciences, the variables are often simple dichotomies, or of only ordinal significance and, consequently, cannot be handled in the same manner as quantitative variables. In this chapter we shall consider the type of latent variable models which have been developed for such data, beginning with an account of the various approaches that have been suggested for the factor analysis of binary variables.