Weight smoothing models to estimate survey estimates from binary data

Abstract

In surveys, when the number of respondents in a post-stratum is small relative to the population size in that post-stratum, post-stratification weights are inflated and modifications are required to obtain less variable estimates. Weight smoothing models, random-effects models that induce shrinkage across post-stratum means, are such modifying methods. We describe the empirical Bayes weight smoothing model approach to estimate the overall mean of a binary survey outcome. The generalized linear mixed model formulation of this model allows easy fitting. Two extensions of the model are presented. The estimation of the prevalence and incidence trend of influenza-like illness using the Great Influenza Survey in Flanders, Belgium, is considered as an application.