Survey Methodology

Abstract

The analysis of survey data from different geographical areas, where the data from each area are polychotomous, can be easily performed using hierarchical Bayesian models even if there are small cell counts in some of these areas. However, there are difficulties when the survey data have missing information in the form of nonresponse especially when the characteristics of the respondents differ from the nonrespondents. We use the selection approach for estimation when there are nonrespondents because it permits inference for all the parameters. Specifically, we describe a hierarchical Bayesian model to analyze multinomial nonignorable nonresponse data from different geographical areas, some of them can be small. For the model, we use a Dirichlet prior density for the multinomial probabilities and a beta prior density for the response probabilities. This permits a “borrowing of strength” of the data from larger areas to improve the reliability in the estimates of the model parameters corresponding to the smaller areas. Because the joint posterior density of all the parameters is complex, inference is sampling based and Markov chain Monte Carlo methods are used. We apply our method to provide an analysis of body mass index (BMI) data from the third National Health and Nutrition Examination Survey (NHANES III). For simplicity, the BMI is categorized into three natural levels, and this is done for each of eight age-race-sex domains and thirty-four counties. We assess the performance of our model using the NHANES III data and simulated examples, which show our model works reasonably well.