A Bayesian model for two-way contingency tables with nonignorable nonresponse from small areas

Abstract

Many surveys provide categorical data and there may be one or more missing categories. We describe a nonignorable nonresponse model for the analysis of two-way contingency tables from small areas. There are both item and unit nonresponse. One approach to analyze these data is to construct several tables corresponding to missing categories. We describe a hierarchical Bayesian model to analyze two-way categorical data from different areas. This allows a borrowing of strength of the data from larger areas to improve the reliability in the estimates of the model parameters corresponding to the small areas. Also we use a nonignorable nonresponse model with Bayesian uncertainty analysis by placing priors in nonidentifiable parameters instead of a sensitivity analysis for nonidentifiable parameters. 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 on thirteen states to obtain the finite population proportions.