A Bayesian Uncertainty Analysis for Nonignorable Nonresponse

• Published in: Current Trends in Bayesian Methodology with Applications pp. 455 - 474
• Format: Book Chapter
• Language: English
• Published: United Kingdom Chapman and Hall/CRC 2015; CRC Press LLC
• Subjects: BIOLOGY, LIFE SCIENCES; Probability & statistics; Population Proportion; Categorical Table; Geweke Test; Bayesian Uncertainty; Missing Data Mechanism; Loglinear Model; CI; Conditional Posterior Densities; Griddy Gibbs Sampler; MNAR Mechanism; Nonignorable Nonresponse; Uncertainty Interval; Conditional Posterior Distributions; Common Positives; Joint Posterior Density; Reversible Jump MCMC Sampler; Nonresponse Model; Joint Probability Mass Function; Supplemental Tables; Posterior Density; Plausible Values; Posterior Distributions; Pattern Mixture Model
• ISBN: 1482235110; 9781482235111
• DOI: 10.1201/b18502-27

We discuss the concept of Bayesian uncertainty analysis in survey sampling for categorical data when there is nonignorable nonresponse. This is important because in sample surveys, data are typically summarized in contingency tables and there are nonresponders. In a nonignorable nonresponse model there are nonidentifiable parameters, and a sensitivity analysis is necessary to study the effects of these parameters on the parameter of interest. The sensitivity analysis is typically performed by setting the nonidentifiable parameters at various plausible values. In a Bayesian uncertainty analysis, rather than performingin Bayesianwe put a prior on the nonidentifiable parameters. We illustrate Bayesian uncertainty analysis using a three-way contingency table (i.e., a single r × c× u table) with nonignorable nonresponse.