Nonparametric Bayesian analysis of a proportion for a small area under nonignorable nonresponse

Abstract

In small area estimation, it is a standard practice to assume that the area effects are exchangeable. This is obtained by assuming that the area effects have a common parametric distribution, and a Bayesian approach is attractive. The Dirichlet process prior (DPP) has been used to provide a nonparametric version of this approach. The DPP is useful because it makes the procedure more robust, and the Bayesian approach helps to reduce the effect of nonidentifiability prominent in nonignorable nonresponse models. Using the DPP, we develop a Bayesian methodology for the analysis of nonignorable nonresponse binary data from many small areas, and for each area, we estimate the proportion of individuals with a particular characteristic. Our DPP model is centered on a baseline model, a standard parametric model. We use Markov chain Monte Carlo methods to fit the DPP model and the baseline model, and our methodology is illustrated using data on victimization in ten domains from the National Crime Survey. Our comparisons show that it may be preferable to use the nonparametric DPP model over the parametric baseline model for the analysis of these data. Email: jwc7@cdc.gov