Bayesian nonparametric latent class analysis with different item types

Abstract

Latent class analysis (LCA) requires deciding on the number of classes. This is traditionally addressed by fitting several models with an increasing number of classes and determining the optimal one using model selection criteria. However, different criteria can suggest different models, making it difficult to reach a consensus on the best criterion. Bayesian nonparametric LCA based on the Dirichlet process mixture (DPM) model is a flexible alternative approach that allows for inferring the number of classes from the data. In this article, we introduce a DPM-based mixed-mode LCA model, referred to as DPM-MMLCA, which clusters individuals based on indicators measured on mixed metrics. We illustrate two algorithms for posterior estimation and discuss inferential procedures to estimate the number of classes and their composition. A simulation study is conducted to compare the performance of the DPM-MMLCA with the traditional mixed-mode LCA under different scenarios. Five design factors are considered, including the number of latent classes, the number of observed variables, sample size, mixing proportions, and class separation. Performance measures include evaluating the correct identification of the number of latent classes, parameter recovery, and assignment of class labels. The Bayesian nonparametric LCA approach is illustrated using three real data examples. Additionally, a hands-on tutorial using R and the nimble package is provided for ease of implementation. (PsycInfo Database Record (c) 2025 APA, all rights reserved).