A Semiparametric Approach to Modeling Nonlinear Relations Among Latent Variables

2005/10/01 by Daniel J. Bauer · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · doi:10.1207/s15328007sem1204_1

openalex publication_date 2005/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

To date, finite mixtures of structural equation models (SEMMs) have been developed and applied almost exclusively for the purpose of providing model-based cluster analyses. This type of analysis constitutes a direct application of the model wherein the estimated component distributions of the latent classes are thought to represent the characteristics of distinct unobserved subgroups of the population. This article instead considers an indirect application of the SEMM in which the latent classes are estimated only in the service of more flexibly modeling the characteristics of the aggregate population as a whole. More specifically, the SEMM is used to semiparametrically model nonlinear latent variable regression functions. This approach is first developed analytically and then demonstrated empirically through analyses of simulated and real data.

Citations

• Measurement Invariance, Factor Analysis and Factorial Invariance
• Three Multivariate Models: Factor Analysis, Latent Structure Analysis, and Latent Profile Analysis
• The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities.
• Maximum Likelihood Estimation of Latent Interaction Effects with the LMS Method
• Bayesian Density Estimation and Inference Using Mixtures

Cited by

• Observations on the Use of Growth Mixture Models in Psychological Research
• Daniel J. Bauer [wikipedia]