Bayesian semiparametric models for nonignorable missing mechanisms in generalized linear models

Semiparametric models provide a more flexible form for modeling the relationship between the response and the explanatory variables. On the other hand in the literature of modeling for the missing variables, canonical form of the probability of the variable being missing (p) is modeled taking a fully parametric approach. Here we consider a regression spline based semiparametric approach to model the missingness mechanism of nonignorably missing covariates. In this model the relationship between the suitable canonical form of p (e.g. probit p) and the missing covariate is modeled through several splines. A Bayesian procedure is developed to efficiently estimate the parameters. A computationally advantageous prior construction is proposed for the parameters of the semiparametric part. A WinBUGS code is constructed to apply Gibbs sampling to obtain the posterior distributions. We show through an extensive Monte Carlo simulation experiment that response model coefficent estimators maintain better (when the true missingness mechanism is nonlinear) or equivalent (when the true missingness mechanism is linear) bias and efficiency properties with the use of proposed semiparametric missingness model compared to the conventional model.