10 - Latent-Class Models

Abstract

This chapter discusses latent-class models. The latent-class models assume that the relationships between several observed discrete variables can be explained by use of a log-linear model involving both these variables and one or more unobserved discrete variables. The usual assumption made in these models is that the manifest variables are conditionally independent given the latent variable or variables so that for any given manifest variable, the other observed variables provide no information on that given variable beyond information provided by the latent variable or variables. In this sense, the latent variables or variables fully account for the observed relationships among the manifest variables. In the traditional latent-class model, one dichotomous or polytomous latent variable and more than one dichotomous or polytomous manifest variables are present. The only assumption made is the local independence assumption that the manifest variables are conditionally independent given the latent variable. The chapter also presents the computation of maximum likelihood estimates, chi-square statistics, and adjusted residuals for the basic latent-class model in which a single latent variable is present and the only assumption made is that the manifest variables are conditionally independent given the latent variable. As with log-linear models, asymptotic variances can be computed through analogies to weighted regression problems.