Categorical latent variable modeling utilizing fuzzy clustering generalized structured component analysis as an alternative to latent class analysis

Abstract

Latent class analysis is becoming popular in many areas of education, psychology, social and behavioral sciences, public health, and medicine. However, it often suffers from identification issues due to the large number of parameters involved when using maximum likelihood (ML) estimation. Increasing the sample size, reducing sparseness, and strengthening the relationship between the observed variables and the latent variables all improve the information and thus reduce the identification issues, but the identification issue still affects the validity of parameter estimates in ML estimation and the definition of identification is not sufficient to guarantee the existence of an ML solution. In this paper, generalized structured component analysis (GSCA), which is a component-based approach that utilizes optimal scaling and fuzzy clustering, is applied to avoid these identification issues and develop more stable solutions for the heterogeneity of a population based on a set of categorical responses. Testing our proposed new approach, component-based (CB) latent class analysis (LCA), on real world substance use data from Add Health produced not only the same features as those yielded by conventional ML LCA but also stable estimation without identification issues. Comparing the results obtained from ML LCA using Mplus and poLCA in R, with those from our proposed CB LCA using GSCA in R revealed a similar number of latent classes and posterior probabilities and only minor discrepancies in individual latent class classifications when the posterior probabilities of membership are not distinct.