Confirmatory Latent Class Analysis: Model Selection Using Bayes Factors and (Pseudo) Likelihood Ratio Statistics

Area of Science:

• Statistics
• Machine Learning
• Psychometrics

Background:

• Latent class models (LCMs) are used for analyzing categorical data by identifying unobserved subgroups.
• Assigning meaningful interpretations to latent classes often requires incorporating inequality constraints on class-specific probabilities.
• Different constraint sets lead to distinct LCMs, necessitating robust model selection techniques.

Purpose of the Study:

• To investigate and compare model selection criteria for latent class models with inequality constraints.
• To evaluate the performance of Bayesian selection criteria against traditional maximum likelihood methods.
• To demonstrate the advantages of Bayesian approaches in avoiding common flaws associated with maximum likelihood selection.

Main Methods:

• Utilizing Bayes factors for Bayesian model selection.
• Employing (pseudo) likelihood ratio statistics evaluated with posterior predictive p-values.
• Conducting a simulation study to assess the properties of different selection criteria under controlled conditions.

Main Results:

• Bayesian selection criteria, specifically Bayes factors and pseudo-likelihood ratio statistics, do not exhibit the same limitations as maximum likelihood based criteria.
• Simulation results indicate that Bayes factors and the pseudo-likelihood ratio statistic possess favorable properties for model selection in this context.
• The proposed Bayesian methods offer a more reliable approach to selecting appropriate latent class models.

Conclusions:

• Bayesian model selection criteria provide a robust alternative to maximum likelihood methods for latent class models with inequality constraints.
• The study highlights the practical utility and superior performance of Bayes factors and pseudo-likelihood ratio statistics.
• The findings are further illustrated with a practical example, demonstrating the application of these methods.