Extended mixture factor analysis model with covariates for mixed binary and continuous responses.

Area of Science:

• Statistical modeling
• Latent variable analysis
• High-dimensional data analysis

Background:

• Finite mixture factor analysis models latent group structures in high-dimensional data.
• Existing models primarily handle continuous responses, limiting application with dichotomous items.
• Dichotomous items are frequently used to define latent domains in practical settings.

Purpose of the Study:

• To propose an extended finite mixture factor analysis model capable of handling mixed continuous and binary responses.
• To develop and validate a robust estimation and convergence monitoring methodology for the proposed model.
• To demonstrate the practical utility of the extended model using real-world data.

Main Methods:

• Utilized an extended finite mixture factor analysis framework incorporating covariates for mixed response types.
• Employed a Monte Carlo Expectation-Maximization (MCEM) algorithm for model parameter estimation.
• Implemented Gibbs sampling for approximating conditional expectations and bridge sampling for convergence diagnostics.

Main Results:

• The MCEM algorithm, with Gibbs and bridge sampling, effectively estimates parameters and monitors convergence for mixed-response factor analysis.
• Model comparison using Bayesian Information Criterion (BIC) with Monte Carlo approximation facilitates model selection.
• Simulation studies confirmed the computational properties of the MCEM algorithm.

Conclusions:

• The proposed extended finite mixture factor analysis model offers a flexible approach for analyzing high-dimensional data with mixed response types.
• The MCEM algorithm with bridge sampling provides a reliable method for parameter estimation and convergence assessment.
• The model demonstrates practical usefulness in analyzing real-world datasets with both continuous and binary variables.