We predict finite population mean BMI nationally for children and adolescents using NHANES III survey data. There are many nonrespondents and no distributional assumption is made on BMI. As link functions for response indicators, we compare the logistic distribution assumption is made on BMI. As link functions for response indicators, we compare the logistic distribution and student’s mixtures. Nonrespondents are assigned cells based on propensity scores to impute BMI, and uncertainty about this process is included. Predictive inference is done using least-squares, and we compare results with a recent method.