Bayesian model comparison for random effects probit models with missing covariates
For model comparison in random effects probit models with incompletely observed covariates, this paper develops a Bayesian data-augmentation workflow in which latent Gaussian responses, random effects, and missing covariate values are updated within a common augmented sampling scheme. Because specifying a fully parametric joint model for mixed continuous and categorical covariates is often unattractive in survey applications, missing covariates are updated by a decision-tree-assisted Bayesian-bootstrap step. Competing models are evaluated conditionally on one common medoid completion using Chib’s method with reduced Gibbs sampling; sensitivity is assessed with respect to the Chib evaluation point, the regression-coefficient prior, and the medoid reference model. The simulation study compares the proposed approach with complete case analysis, multiple imputation by chained equations, missForest single imputation, information criteria, and predictive criteria under MCAR, cross-dependent MAR-type, and self-masked MNAR scenarios. An empirical illustration based on the National Educational Panel Study demonstrates how the method can be used for comparing labor-market models of current employment when competence measures and employment-history covariates are incompletely observed. The results show that missing covariates can materially affect model rankings, and that the proposed workflow provides a transparent evidence-based comparison of nested and non-nested random effects probit specifications under incomplete covariate information.