Nonparametric Bayesian Models to Handle Nonresponse in Large Scale Panel Studies with Refreshment Samples

Abstract:

Panel studies typically suffer from nonresponse, especially attrition. Ignoring the attrition can result in biased inferences if the missing data is 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 propose Bayesian latent pattern mixture models, for which attrition and survey variables are modeled jointly via latent classes to handle unit and item nonresponse simultaneously under the framework of multiple imputation in a two wave panel with one refreshment sample. This approach features a Dirichlet process mixture of multinomial distributions for the involved categorical variables under high dimension and complex dependency structure. We apply the procedure to the 2007-2008 Associated Press/Yahoo News election panel study and present the bias-corrected inference when the attrition effect is diagnosed as non-ignorable. Our proposed fully nonparametric Bayesian procedure captures all sources of uncertainty and demonstrates the flexibility of representing an open-ended framework for robust model-based survey inference.