Semiparametric Bayesian analysis of structural equation models with fixed covariates.

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Structural Equation Models (SEMs) commonly assume normal distributions for latent variables.
• This normality assumption is frequently violated in biomedical research, limiting SEM applicability.
• There is a need for robust SEM methods that accommodate non-normal latent variable distributions.

Purpose of the Study:

• To develop a semiparametric Bayesian approach for SEMs that relaxes the normality assumption for latent variables.
• To provide a general Bayesian framework for SEMs with covariates and non-normal latent variables.
• To enhance the utility of SEMs in biomedical research where distributional assumptions may not hold.

Main Methods:

• A semiparametric hierarchical modeling framework is proposed for latent variables.
• An approximate truncation Dirichlet process prior distribution is specified for latent variables.
• Efficient posterior analysis is achieved using stick-breaking priors and a blocked Gibbs sampler.

Main Results:

• The developed methodology is successfully applied to a study of kidney disease in diabetes patients.
• A simulation study demonstrates the empirical performance and validity of the proposed semiparametric Bayesian approach.
• The approach effectively handles non-normal latent variable distributions in SEMs.

Conclusions:

• The proposed semiparametric Bayesian approach offers a flexible alternative to traditional SEMs when normality assumptions are violated.
• This method enhances the reliability of SEMs in complex biomedical research settings.
• The approach provides a valuable tool for analyzing latent variables in diverse scientific fields.