Semiparametric Bayesian inference on generalized linear measurement error models

The classical assumption in generalized linear measurement error models (GLMEMs) is that measurement errors (MEs) for covariates are distributed as a fully parametric distribution such as the multivariate normal distribution. This paper uses a centered Dirichlet process mixture model to relax the fully parametric distributional assumption of MEs, and develops a semiparametric Bayesian approach to simultaneously obtain Bayesian estimations of parameters and covariates subject to MEs by combining the stick-breaking prior and the Gibbs sampler together with the Metropolis–Hastings algorithm. Two Bayesian case-deletion diagnostics are proposed to identify influential observations in GLMEMs via the Kullback–Leibler divergence and Cook’s distance. Computationally feasible formulae for evaluating Bayesian case-deletion diagnostics are presented. Several simulation studies and a real example are used to illustrate our proposed methodologies.