Bayesian Latent Class Models for Multiple Imputation of Multivariate Categorical Data Under Ignorable Missingness Mechanism

Missing data are a pervasive challenge in the analysis of multivariate categorical data and can lead to biased estimation and reduced statistical efficiency when handled inappropriately. Bayesian latent class multiple imputation provides a flexible framework for addressing this problem by exploiting the underlying latent structure of the data. However, conventional Bayesian latent class imputation models generally assume that latent class membership is independent of observed covariates, potentially limiting estimation accuracy when covariates are informative of the latent class structure. This study proposes a covariate-dependent Bayesian latent class model for multiple imputation under the MAR mechanism. The proposed approach models latent class membership using multinomial logistic regression, allowing observed covariates to influence class allocation while preserving the latent class formulation for the response variables. Bayesian inference is performed using Gibbs sampling, with Pólya--Gamma data augmentation facilitating efficient posterior estimation of the regression coefficients. The performance of the proposed model was evaluated through a comprehensive simulation study under varying strengths of covariate effects and sample sizes, and compared with the conventional Bayesian latent class model. Performance was assessed using multiple imputation inference, latent class proportion recovery, regression coefficient recovery, posterior stability, and empirical coverage probabilities. The proposed model produced unbiased inference and demonstrated improved estimation accuracy when covariates were associated with latent class membership, while maintaining performance comparable to the conventional model when covariate effects were absent. Furthermore, RMSE decreased consistently as the sample size increased, providing empirical evidence of posterior concentration and improved estimation precision. These findings demonstrate that incorporating covariates into Bayesian latent class multiple imputation provides a practical and effective extension of the conventional latent class framework for multivariate categorical data with missing values under the MAR mechanism.