Semi-parametric Selection Models for Potentially Non-ignorable Attrition in Panel Studies with Refreshment Samples

Panel studies typically suffer from attrition. Ignoring the attrition can result in biased inferences if the missing data are systematically related to outcomes of interest. Unfortunately, panel data alone cannot inform the extent of bias due to attrition. Many panel studies also include refreshment samples, which are data collected from a random sample of new individuals during the later waves of the panel. Refreshment samples offer information that can be utilized to correct for biases induced by non-ignorable attrition while reducing reliance on strong assumptions about the attrition process. We present a Bayesian approach to handle attrition in two-wave panels with one refreshment sample and many categorical survey variables. The approach includes (1) an additive non-ignorable selection model for the attrition process; and (2) a Dirichlet process mixture of multinomial distributions for the categorical survey variables. We present Markov chain Monte Carlo algorithms for sampling from the posterior distribution of model parameters and missing data. We apply the model to correct attrition bias in an analysis of data from the 2007G«Ù08 Associated Press/Yahoo News election panel study.