Multiple imputation for high-dimensional mixed incomplete continuous and binary data

Abstract

It is common in applied research to have large numbers of variables measured on a modest number of cases. Even with low rates of missingness of individual variables, such data sets can have a large number of incomplete cases with a mix of data types. Here, we propose a new joint modeling approach to address the high-dimensional incomplete data with a mix of continuous and binary data. Specifically, we propose a multivariate normal model encompassing both continuous variables and latent variables corresponding to binary variables. We apply a parameter-extended Metropolis–Hastings algorithm to generate the covariance matrix of a mixture of continuous and binary variables. We also introduce prior distribution families for unstructured covariance matrices to reduce the dimension of the parameter space. In several simulation settings, the method is compared with available-case analysis, a rounding method, and a sequential regression method.