Sequential Hierarchical Regression Imputation

Abstract

Skip patterns, bounds, and diverse measurement scales often exacerbate the problem of item nonresponse in the analysis of survey data. Sequential, or variable-by-variable imputation techniques have been quite successfully applied to overcome such problems. Most of these techniques have so far focused on relatively simple designs, and studies have demonstrated the consistency of these methods with techniques that draw from a joint posterior predictive distribution of missing data. Here we consider a sequential imputation technique based on a family of hierarchical regression models, extending the sequential approach to correlated data, (e.g., clustered data) and assess its performance. Each of the regression models is tailored to the variable being handled. Computational techniques used to approximate the posterior predictive distributions are based on Markov Chain Monte Carlo (MCMC) and numerical integration to overcome the problem of intractability. We present a simulation study assessing the compatibility of this approach with the joint data generation mechanism. In the scenarios studied, the sequential method leads to well-calibrated estimates and often performs better than methods that are currently available to practitioners.