Using Auxiliary Marginal Distributions in Imputations for Nonresponse while Accounting for Survey Weights, with Application to Estimating Voter Turnout

Abstract

In many survey settings, population counts or percentages are available for some of the variables in the survey, for example, from censuses, administrative databases, or other high-quality surveys. We present a model-based approach to utilize such auxiliary marginal distributions in multiple imputation for unit and item nonresponse in complex surveys. In doing so, we ensure that the imputations produce design-based estimates that are plausible given the known margins. We introduce and utilize a hybrid missingness model comprising a pattern mixture model for unit nonresponse and selection models for item nonresponse. We also develop a computational strategy for estimating the parameters of and generating imputations with hybrid missingness models. We apply a hybrid missingness model to examine voter turnout by subgroups using the 2018 Current Population Survey for North Carolina. The hybrid missingness model also facilitates modeling measurement errors simultaneously with handling missing values. We illustrate this feature with the voter turnout application by examining how results change when we allow for overreporting, that is, individuals self-reporting that they voted when in fact they did not.