Using auxiliary marginal distributions in imputations for nonresponse while accounting for survey weights, with application to estimating voter turnout

TL;DR

This paper develops a model-based multiple imputation method incorporating known voter turnout and demographic margins to address nonresponse bias in survey data, ensuring plausible estimates aligned with known population totals.

Contribution

It introduces a hybrid missingness model combining pattern mixture and selection models to improve imputation accuracy in survey nonresponse scenarios.

Findings

Simulation studies demonstrate robust performance under various missingness assumptions.

Application to 2018 CPS data reveals voter turnout patterns by subgroup.

Sensitivity analysis shows impact of over-reporting on turnout estimates.

Abstract

The Current Population Survey is the gold-standard data source for studying who turns out to vote in elections. However, it suffers from potentially nonignorable unit and item nonresponse. Fortunately, after elections, the total number of voters is known from administrative sources and can be used to adjust for potential nonresponse bias. We present a model-based approach to utilize this known voter turnout rate, as well as other population marginal distributions of demographic variables, in multiple imputation for unit and item nonresponse. 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. Using simulation studies, we illustrate repeated sampling performance of the model under different assumptions about the missingness mechanisms. We apply the model to examine voter turnout by subgroups using the 2018 Current Population Survey for North Carolina. As a sensitivity analysis, we examine how results change when we allow for over-reporting, i.e., individuals self-reporting that they voted when in fact they did not.