Hierarchical Bayesian nonignorable nonresponse regression models for small areas: An application to the NHANES data - ARCHIVED

We use hierarchical Bayesian models to analyze body mass index (BMI) data of children and adolescents with nonignorable nonresponse from the Third National Health and Nutrition Examination Survey (NHANES III). Our objective is to predict the finite population mean BMI and the proportion of respondents for domains formed by age, race and sex (covariates in the regression models) in each of thirty five large counties, accounting for the nonrespondents. Markov chain Monte Carlo methods are used to fit the models (two selection and two pattern mixture) to the NHANES III BMI data. Using a deviance measure and a cross-validation study, we show that the nonignorable selection model is the best among the four models. We also show that inference about BMI is not too sensitive to the model choice. An improvement is obtained by including a spline regression into the selection model to reflect changes in the relationship between BMI and age.