Bayesian model comparison of nonlinear structural equation models with missing continuous and ordinal categorical...

Area of Science:

• Behavioral Science
• Psychological Research
• Statistical Modeling

Background:

• Missing data frequently occur in behavioral and psychological research, posing challenges for accurate analysis.
• Existing methods may not adequately address complex data structures with both continuous and categorical variables.

Purpose of the Study:

• To develop a robust Bayesian approach for structural equation models with missing continuous and ordinal data.
• To evaluate the accuracy and model selection performance of the proposed Bayesian method.

Main Methods:

• A hybrid algorithm combining Gibbs sampling and Metropolis-Hastings was developed to treat missing data as latent variables.
• Bayesian model comparison using Bayes factors and path sampling was implemented.
• A simulation study and a real-world dataset analysis were conducted.

Main Results:

• Bayesian estimates demonstrated high accuracy in the simulation study.
• The proposed method significantly improved the selection of the correct model when incomplete data were utilized compared to ignoring them.
• The methodology proved effective in analyzing a real dataset on an AIDS preventative intervention.

Conclusions:

• The developed Bayesian approach offers an accurate and effective solution for handling missing data in complex behavioral and psychological research.
• Incorporating incomplete records enhances model selection accuracy, leading to more reliable research findings.
• This method provides a valuable tool for researchers dealing with incomplete datasets in various scientific domains.