JSM 2005 - Toronto

Abstract #302288

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 45
Type: Invited
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #302288
Title: A Hierarchical Bayesian Nonresponse Model for Two-way Categorical Data from Small Areas with Uncertainty about Ignorability
Author(s): Myron Katzoff*+ and Balgobin Nandram
Companies: National Center for Health Statistics and Worcester Polytechnic Institute
Address: 3311 Toledo Road, Hyattsville, MD, 20782,
Keywords: Metropolis-Hastings Sampler ; SIR Algorithm ; Nonignorable Nonresponse Model ; Expansion Model
Abstract:

In this paper, we study the problem of nonignorable nonresponse in a two-dimensional contingency table that can be constructed for each of several small areas when there is both item and unit nonresponse. We conceptualize the full data array to consist of a table for complete data and three supplemental tables for missing row data, missing column data, and missing row and column data. For nonignorable nonresponse, the response probabilities are allowed to vary by area, cell, and these three types of "missingness." The cell probabilities for each area are generated from a common distribution, and their similarity across the areas is parametrically quantified. Our approach is an extension of the selection approach for nonignorable nonresponse (Nandram and Choi 2002) for binary data. The extension is an expansion model centered on an ignorable nonresponse model so that the probability of a response is dependent upon which of the categories is the response. Our investigation employs hierarchical Bayesian models and Markov Chain Monte Carlo computational methods for posterior inference. Models and methods are illustrated with data from the NHANES III survey.

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Revised March 2005