Bayesian Inference of the Cell Probabilities of a Two-Way Categorical Table Under Non Ignorability

Abstract

Given data from a two-way categorical table, we show how to make inference about the cell probabilities using a Bayesian method when there is non ignorable non response. The problem is usually formulated with four sub-tables, one with the complete cases and the remaining three sub-tables with the incomplete cases. A recent Bayesian method has been used to ease the problem of over-parameterization, but as expected, there is loss in efficiency in estimating the cell probabilities. In a new Bayesian method we have collapsed the three tables with the incomplete cases into a single table. We use three examples and a simulation study to show the superiority of the second method over the first method.