Distinguishing Between Latent Classes and Continuous Factors: Resolution by Maximum Likelihood?

2006/12/01 by Gitta H. Lubke, Gitta Lubke, Michael C. Neale · 460 citations
Computer Science · Mathematics · #Advanced Statistical Modeling Techniques #Artificial intelligence #Bayesian Methods and Mixture Models #Categorical variable #Computer science #Econometrics #Latent class model #Latent variable #Latent variable model #Local independence #Mathematics #Population #Probabilistic latent semantic analysis #Sample size determination #Statistical Methods and Bayesian Inference #Statistics #Structural equation modeling #Variable (mathematics)

paper · doi:10.1207/s15327906mbr4104_4

published in Multivariate Behavioral Research 41(4), 499-532 (Taylor & Francis)

openalex publication_date 2006/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an underlying latent variable is continuous or categorical, and (b) to quantify the effect of sample size and class proportions on making this distinction. Latent variable models with categorical, continuous, or both types of latent variables are fitted to simulated data generated under different types of latent variable models. If an analysis is restricted to fitting continuous latent variable models assuming a homogeneous population and data stem from a heterogeneous population, overextraction of factors may occur. Similarly, if an analysis is restricted to fitting latent class models, overextraction of classes may occur if covariation between observed variables is due to continuous factors. For the data-generating models used in this study, comparing the fit of different exploratory factor mixture models usually allows one to distinguish correctly between categorical and/or continuous latent variables. Correct model choice depends on class separation and within-class sample size.

Citations

• Testing the number of components in a normal mixture
• "General Intelligence," Objectively Determined and Measured
• Factor Analysis and AIC

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