Semiparametric Bayesian multiple imputation for regression models with missing mixed continuous-discrete covariates (Q2183768)

This article develops a semiparametric Bayesian approach for regression models with missing mixed continuous and discrete covariates. A Bayesian multiple imputation framework is proposed to deal with incompletely observed mixed-scale variables in the covariate distribution, without a full conditional specification. The model formulation involves a substantive model, the regression model whose parameters are the researchers' main interest, and conditionally modeling incompletely observed covariates. In the nonparametric Bayesian specification, the covariates joint distribution of the missing variables is specified using the probit stick-breaking process mixture (PSBPM) model, which allows for stickbreaking weights varying depending on the predictors. To deal with the discrete variables, continuous latent variables are introduced. Mixed-scale variables are expressed through the transformation of the latent continuous variables. Four simulation studies are conducted to illustrate the good performance of the proposed method, specifically when multiple imputation by chained equation with full conditional specification cannot draw from a Bayesian joint model: linear regression with a quadratic term, linear regression with an interaction term, proportional hazards model with a binary covariate, and logistic regression with a binary covariate. An application of the method to the Alzheimer's Disease Neuroimaging Initiative dataset is also presented.