Bayesian Analysis for Cluster Sampling

• Activity Number: 101
• Type: Invited
• Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Susanna Makela* and Yajuan Si and Andrew Gelman
• Companies: Columbia University and University of Wisconsin - Madison and Columbia University
• Keywords: Bayesian ; Cluster Sampling ; Probability proportional to size ; Hierarchical ; Model-based

Abstract

We develop a Bayesian framework for finite population inference under cluster sampling in a design-based survey context. The two-stage sampling design proceeds by first selecting clusters with probability proportional to cluster sizes and second randomly sampling units out of selected clusters. We incorporate the sampling design into multilevel modeling framework to account for the cluster structure and generalize the inference for nonsampled clusters. The cluster sizes will be treated as covariates. We consider both scenarios when the nonsampled cluster sizes are known and unknown, that is, when the sampling probabilities are known and unknown for the nonsampled units. We will estimate the unknown cluster sizes and simultaneously include them as predictors in a flexible hierarchical regression framework with weekly informative prior information. We use simulation studies to evaluate the performance of our procedure and compare it to the classical design-based estimator. We apply our method to the Fragile Family and Child Wellbeing Study. The model-based framework will fully account for the uncertainties and yield robust inference that is design-consistent.