# Seminars
## General Departmental Seminar Series
### Robust Models for Surveys with
Differential Probabilities of Inclusion
Roderick Little, Department of Biostatistics
University of Michigan
Friday, Nov 10, 2000, 12:00-1:00 pm
K6/124 Clinical Sciences Center, 600 Highland Avenue
ABSTRACT
Sample surveys often yield units with differential probabilities of inclusion, because the probability of being selected into the sample is not constant, or because the probability of responding given selection varies across units. The standard design-based analysis is to weight responding units by the inverse of the (possibly estimated ) probability of inclusion. This weighting approach is simple and corrects for selection bias if the inclusion probability is known or well estimated. However, it can yield estimates with high variance, as when the weights are very variable or a high weight multiplies an extreme value of a survey outcome. Large weights are often trimmed back to a maximum value (say 3) to reduce weight variability and control variance, but this practice is somewhat ad-hoc.
I discuss a Bayesian approach to the analysis of surveys with differential probabilities of inclusion based on multilevel models involving subclasses indexed by the probability of inclusion. These models yield the standard weighted estimates as special cases, but provide a principled approach to variance reduction. The range of models we can consider in practice has been greatly expanded by modern simulation tools for Bayesian inference such as Markov-Chain Monte Carlo. The approach can be applied to a number of settings involving differential inclusion, including stratified sampling, differential selection where the selection probability is known only for sampled units, post-stratification, probability is known only for sampled units, post-stratification, probability proportional to size sampling, unit nonresponse, and raking to sets of margins.
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