A Bayesian uncertainty analysis for nonignorable nonresponse in two-way contingency table

Abstract

We study the problem of nonignorable nonresponse in a two-way contingency table and there may be one or two missing categories. We describe a nonignorable nonresponse model for the analysis of two-way categorical table. One approach to analyze these data is to construct several tables (one complete and the others incomplete). There are nonidentifiable parameters in incomplete tables. We describe a hierarchical Bayesian model to analyze two-way categorical data. We use a nonignorable nonresponse model with Bayesian uncertainty analysis by placing priors in nonidentifiable parameters instead of a sensitivity analysis for nonidentifiable parameters. To reduce the effects of nonidentifiable parameters, we project the parameters to a lower dimensional space and we allow the reduced set of parameters to share a common distribution. We use the griddy Gibbs sampler to fit our models and compute DIC and BPP for model diagnostics. We illustrate our method using data from NHANES III data to obtain the finite population proportions.