Parameter-expanded data augmentation for analyzing correlated binary data using multivariate probit models

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Data augmentation is common for analyzing correlated binary data using multivariate probit models in Bayesian analysis.
• The identification issue in these models requires complex Metropolis-Hastings algorithms, leading to slow convergence and inefficient Markov chains.
• Parameter-expanded data augmentation can improve mixing and convergence by introducing artificial parameters.

Purpose of the Study:

• To develop efficient parameter-expanded data augmentation algorithms for multivariate probit models.
• To investigate both identifiable and non-identifiable multivariate probit models.
• To improve the convergence and mixing of correlation parameters in Bayesian analysis.

Main Methods:

• Developed parameter-expanded data augmentation algorithms for both identifiable and non-identifiable multivariate probit models.
• Applied these methods to analyze correlated binary data.
• Utilized simulation studies and a real-world longitudinal dataset (Six Cities study) for illustration.

Main Results:

• Parameter-expanded approaches based on non-identifiable models circumvent the need for a Metropolis-Hastings algorithm for correlation matrix sampling.
• These methods enhance the convergence and mixing of correlation parameters.
• The identifiable model approach may yield regression parameters with smaller standard errors compared to the non-identifiable model.

Conclusions:

• Parameter-expanded data augmentation offers an efficient alternative for analyzing correlated binary data with multivariate probit models.
• The proposed methods successfully improve computational efficiency and parameter mixing.
• Both identifiable and non-identifiable model approaches have distinct advantages for specific analytical goals.