Latent class cluster analysis

Abstract

This paper describes the technique of exploratory latent class cluster analysis. The classical analysis is a model-based statistical approach for identifying unobserved subgroups from observed categorical data and for classifying cases into the identified subgroups based on membership probabilities estimated directly from the statistical model.

In the first part on mathematical modeling of the paper, we introduce the data and the sampling distribution for the data as required in the analysis of latent classes, the fundamental model assumptions are reviewed, and the general unrestricted latent class model is presented. Classification of cases into the clusters using modal assignment is discussed. In the second part on inferential statistics of the paper, we briefly review the classical maximum likelihood methodology related to parameter estimation and model testing, and the information criteria AIC and SIC for model selection. In the third part on case study of the paper, the General Social Survey data are analyzed using the software Latent GOLD^®. We present the Latent GOLD^® profile plot and tri plot options for the graphical representation of the results. The Latent GOLD^® classification output illustrating the assignment of respondents to the latent survey respondent types is also shown.