A Bayesian Analysis of BMI Data of Children from Small Domains: Adjustment for Nonresponse

We analyze data on body mass index (BMI) in the third National Health and Nutrition Examination survey, predict finite population BMI stratified by different domains of race, sex and family income, and investigate what adjustment needed for nonresponse mechanism. We built two types of models to analyze the data. In the ignorable nonresponse models, each model is within the hierarchical Bayesian framework. For Model 1, BMI is only related to age. For Model 2, the linear regression is height on weight, and weight on age. The parameters, nonresponse and the nonsampled BMI values are generated from each model. We mainly use the composition method to obtain samples for Model 1, and Gibbs sampler to generate samples for Model 2. We also built two nonignorable nonresponse models corresponding to the ignorable nonresponse models. Our nonignorable nonresponse models have one important feature: the response indicators are not related to BMI and neither weight nor height, but we use the same parameters corresponding to the ignorable nonresponse models. We use sample important resampling (SIR) algorithm to generate parameters and nonresponse, nonsample values. Our results show that the ignorable nonresponse Model 2 (modeling height and weight) is more reliable than Model 1 (modeling BMI), since the predicted finite population mean BMI of Model 1 changes very little with age. The predicted finite population mean of BMI is affected by different domain of race, sex and family income. Our results also show that the nonignorable nonresponse models infer smaller standard deviation of regression coefficients and population BMI than in the ignorable nonresponse models. It is due to the fact that we are incorporating information from the response indicators, and there are no additional parameters. Therefore, the nonignorable nonresponse models allow wider inference