Applications of Nonparametric Hierarchical Models to Surveys with Clustered Outcome

• Activity Number: 234
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Hui Zheng*+ and Roderick Joseph Little
• Companies: Harvard University Medical School and University of Michigan
• Keywords: weighting ; REML ; empirical Bayes estimation

Abstract

The Horvitz-Thompson (HT) estimator is a design-unbiased estimator of finite population totals in probability sampling designs. From a modeling perspective, the Htestimator performs well when the ratios of the outcome values and the inclusion probabilities are exchangeable. When this assumption is not met, the HT estimator can be inefficient. Previously, we used penalized splines (p-splines) to model nonparametric relationships between the outcome and the design variables in one-stage PPS samples. In this presentation, we extend this approach to two-stage designs where outcome are correlated. We use a p-spline mixed model to fit a nonparametric function that relates the mean of the outcome variable to cluster- or unit-level variables while incorporating clustering effects. For inference, we consider the empirical Bayes model-based variance, the jackknife and balanced repeated replicate methods. Simulations show the nonparametric mixed model can provide point estimations with improved efficiency over HT or linear model-assisted estimators. Better inference can also be achieved by producing narrower confidence intervals with satisfactory coverage rates.