A Bayesian model averaging approach to analyzing categorical data with nonignorable nonresponse

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In many surveys, the goal is to estimate the proportion of the population with a certain characteristic of interest. This estimation problem is often complicated by survey nonresponse and the difficulty in modeling the nonresponse mechanism. In this paper, a new method is developed for analyzing categorical data with nonresponse when there is uncertainty about ignorability, which incorporates the idea that there are many a priori plausible ignorable and nonignorable nonresponse models. A class of saturated submodels of the full, nonidentifiable likelihood, containing models which have mixtures of ignorable and nonignorable components is considered, and Bayesian averaging is used to incorporate model uncertainty. This approach is then extended by using uniform priors on model components which do not fit into the partition structure. This method is illustrated using data from the 2000 Accuracy and Coverage Evaluation Survey. A simulation study is used to evaluate the performance of this method and to compare it to other popular nonignorable Bayesian models. The results of the simulation study show that the proposed method generates point estimates which can have reduced mean squared error, and credible intervals which are often, on average, narrower, and which contain the true value of the parameter more frequently, as compared to other nonignorable models, and hence provides a better method for quantifying the additional uncertainty due to the missing data.