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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.

Often, government agencies and survey organizations know the population counts or percentages for some of the variables in a survey. These may be available from auxiliary sources, for example, administrative databases or other high quality surveys. We present and illustrate a model-based framework for leveraging such auxiliary marginal information when handling unit and item nonresponse. We show how one can use the margins to specify different missingness mechanisms for each type of nonresponse. We use the framework to impute missing values in voter turnout in a subset of data from the U.S.\ Current Population Survey (CPS). In doing so, we examine the sensitivity of results to different assumptions about the unit and item nonresponse., Comment: 23 pages, 8 figures

Many panel studies collect refreshment samples---new, randomly sampled respondents who complete the questionnaire at the same time as a subsequent wave of the panel. With appropriate modeling, these samples can be leveraged to correct inferences for biases caused by non-ignorable attrition. We present such a model when the panel includes many categorical survey variables. The model relies on a Bayesian latent pattern mixture model, in which an indicator for attrition and the survey variables are modeled jointly via a latent class model. We allow the multinomial probabilities within classes to depend on the attrition indicator, which offers additional flexibility over standard applications of latent class models. We present results of simulation studies that illustrate the benefits of this flexibility. We apply the model to correct attrition bias in an analysis of data from the 2007-2008 Associated Press/Yahoo News election panel study.

In some contexts, mixture models can fit certain variables well at the expense of others in ways beyond the analyst's control. For example, when the data include some variables with non-trivial amounts of missing values, the mixture model may fit the marginal distributions of the nearly and fully complete variables at the expense of the variables with high fractions of missing data. Motivated by this setting, we present a mixture model for mixed ordinal and nominal data that splits variables into two groups, focus variables and remainder variables. The model allows the analyst to specify a rich sub-model for the focus variables and a simpler sub-model for remainder variables, yet still capture associations among the variables. Using simulations, we illustrate advantages and limitations of focused clustering compared to mixture models that do not distinguish variables. We apply the model to handle missing values in an analysis of the 2012 American National Election Study, estimating relationships among voting behavior, ideology, and political party affiliation., Comment: Supplementary material available from the first author upon request

Panel studies typically suffer from attrition, which reduces sample size and can result in biased inferences. It is impossible to know whether or not the attrition causes bias from the observed panel data alone. Refreshment samples - new, randomly sampled respondents given the questionnaire at the same time as a subsequent wave of the panel - offer information that can be used to diagnose and adjust for bias due to attrition. We review and bolster the case for the use of refreshment samples in panel studies. We include examples of both a fully Bayesian approach for analyzing the concatenated panel and refreshment data, and a multiple imputation approach for analyzing only the original panel. For the latter, we document a positive bias in the usual multiple imputation variance estimator. We present models appropriate for three waves and two refreshment samples, including nonterminal attrition. We illustrate the three-wave analysis using the 2007-2008 Associated Press-Yahoo! News Election Poll., Comment: Published in at http://dx.doi.org/10.1214/13-STS414 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)