The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities.

2004/03/01 by Daniel J. Bauer, Patrick J. Curran · 7 citations
Mathematics · Computer Science · #Statistical Methods and Bayesian Inference #Advanced Statistical Modeling Techniques #Bayesian Methods and Mixture Models

paper · doi:10.1037/1082-989x.9.1.3

openalex publication_date 2004/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model, nonnormal continuous measures, and nonlinear relationships among observed and/or latent variables. When the objective of a SEMM analysis is the identification of latent classes, these conditions should be considered as alternative hypotheses and results should be interpreted cautiously. However, armed with greater knowledge about the estimation of SEMMs in practice, researchers can exploit the flexibility of the model to gain a fuller understanding of the phenomenon under study.

Citations

• Theory-Testing in Psychology and Physics: A Methodological Paradox
• Three Multivariate Models: Factor Analysis, Latent Structure Analysis, and Latent Profile Analysis
• Testing the number of components in a normal mixture
• Bayesian Density Estimation and Inference Using Mixtures
• Distributional Assumptions of Growth Mixture Models: Implications for Overextraction of Latent Trajectory Classes.
• "General Intelligence," Objectively Determined and Measured
• Integrating Person‐Centered and Variable‐Centered Analyses: Growth Mixture Modeling With Latent Trajectory Classes

Cited by

• Diagnostic Procedures for Detecting Nonlinear Relationships Between Latent Variables
• Observations on the Use of Growth Mixture Models in Psychological Research
• A Semiparametric Approach to Modeling Nonlinear Relations Among Latent Variables
• Model selection and psychological theory: A discussion of the differences between the Akaike information criterion (AIC) and the Bayesian information criterion (BIC).
• Attempted Validation of the Scores of the VARK: Learning Styles Inventory With Multitrait–Multimethod Confirmatory Factor Analysis Models
• Profiling authoritarian leaders and followers
• Daniel J. Bauer [wikipedia]