Spline Models for the Population Total from PPS Samples: The Precision Gain from Knowing the Sizes of Nonsampled Units

• Activity Number: 191
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Sahar Z. Zangeneh*+ and Roderick Joseph Little
• Companies: University of Michigan and University of Michigan
• Keywords: Probability proportional to size sampling ; Penalized Spline ; Bayesian Bootstrap

Abstract

In probability proportional to size sampling, sizes for non-sampled (NS) units are not required for the usual Horvitz-Thompson (HT) or Hajek estimates, and this information is rarely included in public use data files. However, Zheng and Little (2005 JOS) show that including the sizes of the NS units as predictors in a spline model can result in improved estimates of the finite population total. We use a penalized spline model to predict the outcome for the NS units based on the predicted sizes. We compare the precision of the HT and Bayesian estimates when the population sizes of NS units are (a) known, and (b) estimated, using a Bayesian Bootstrap model with weakly informative priors. The variance of the latter estimator can be decomposed into one component from estimating the NS sizes and one from the spline model, allowing us to assess the gain in information with available NS sizes.