2025/02/10 by Dongho Shin, Shin, Dongho, Yongyun Shin +1
Mathematics · #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2502.07033
This article focuses on Bayesian estimation of a hierarchical linear model (HLM) from incomplete data assumed missing at random where continuous covariates C and discrete categorical covariates D have interaction effects on a continuous response R. Given small sample sizes, maximum likelihood estimation is suboptimal, and existing Gibbs samplers are based on a Bayesian joint distribution compatible with the HLM, but impute missing values of C and the underlying latent continuous variables D^* of D by a Metropolis algorithm via proposal normal densities having constant variances while the target conditional distributions of C and D have nonconstant variances. Therefore, the samplers are neither guaranteed to be compatible with the joint distribution nor ensured to always produce unbiased estimation of the HLM. We assume a Bayesian joint distribution of parameters and partially observed variables, including correlated categorical D, and introduce a compatible Gibbs sampler that draws parameters and missing values directly from the exact posterior distributions. We apply our sampler to incompletely observed longitudinal data from the small number of patient-physician encounters during office visits, and compare our estimators with those of existing methods by simulation.