Bayesian pattern mixture model under nonignorable nonresponse for binary data

Abstract

We consider a Bayesian pattern mixture model to estimate the proportion of the finite population with missing data. The pattern mixture approach is a way to model missing data. We describe the Bayesian model considering two cases for the parameter of a prior distribution. To fit the model, we use Markov chain Monte Carlo methods. We use the Gibbs sampler with grid method to get the samples of the parameters. We use the National Crime Survey data summarized by Stasny (1991) to estimate the proportion of the finite population. When considering two cases of the parameter of a prior distribution, we saw that the inference for the parameter was not sensitive in our proposed model.