Latent Class Analysis

The basic idea underlying latent class (LC) analysis is a very simple one: some of the parameters of a postulated statistical model differ across unobserved subgroups. These subgroups form the categories of a categorical latent variable (see entry latent variable). This basic idea has several seemingly unrelated applications, the most important of which are clustering, scaling, density estimation, and random-effects modeling. Outside social sciences, LC models are often referred to as finite mixture models. LC analysis was introduced in 1950 by Lazarsfeld, who used the technique as a tool for building typologies (or clustering) based on dichotomous observed variables. More than 20 years later, Goodman (1974) made the model applicable in practice by developing an algorithm for obtaining maximum likelihood estimates of the model parameters. He also proposed extensions for polytomous manifest variables and multiple latent variables, and did important work on the issue of model identification. During the same period, Haberman (1979) showed the connection between LC models and log-linear models for frequency tables with missing (unknown) cell counts. Many important extensions of the classical LC model have been proposed since then, such as models containing (continuous) covariates, local dependencies, ordinal variables, several latent variables, and repeated measures. A general framework for categorical data analysis with discrete latent variables was proposed by Hagenaars (1990) and extended by Vermunt (1997). While in the social sciences LC and finite mixture models are conceived primarily as tools for categorical data analysis, they can be useful in several other areas as well. One of these is density estimation, in which one makes use of the fact that a complicated density can be approximated as a finite mixture of simpler densities. LC analysis can also be used as a probabilistic cluster analysis tool for continuous observed variables, an approach that offers many advantages over traditional cluster techniques such as K-means clustering (see latent profile model). Another application area is dealing with unobserved heterogeneity, for example, in regression analysis with dependent observations (see non-parametric random-effects model).