A Bayesian analysis of mixture structural equation models with non-ignorable missing responses and covariates

Area of Science:

• Behavioral science
• Biomedical science
• Social-psychological science

Background:

• Latent variables and heterogeneous data are common in behavioral, biomedical, and social-psychological sciences.
• Mixture structural equation models (SEMs) are effective for analyzing such data.
• Missing data, including responses and covariates, pose significant challenges in practical research.

Purpose of the Study:

• To develop a Bayesian approach for mixture SEMs with an unknown number of components.
• To address non-ignorable missing responses and covariates within mixture SEMs.
• To incorporate a multinomial logit model to assess covariate influence on component probabilities.

Main Methods:

• A Bayesian framework was developed for mixture SEMs.
• A multinomial logit model was integrated to handle covariate effects on component probabilities.
• A modified Deviance Information Criterion (DIC) was used for model selection.

Main Results:

• Simulation studies demonstrated the accuracy of Bayesian estimates.
• The modified DIC effectively identified the correct number of components.
• The model selection procedure successfully identified appropriate missing data mechanisms.

Conclusions:

• The proposed Bayesian approach is accurate for analyzing mixture SEMs with non-ignorable missing data.
• The model selection procedure aids in determining the correct model structure and missing data handling.
• The methodology is applicable to real-world data, as illustrated by a longitudinal polydrug use study.