Random-Effects Models for Smoothing Poststratification Weights

Laura C. Lazzeroni and Roderick J.A. Little

Abstract:
Poststratification is a common technique for adjusting survey data using external data from a census or larger survey. When the respondent counts in the poststrata are small, modifications of the method, such as collapsing over adjacent poststrata, are needed to reduce variability in the poststratification weights. We consider here inference about a population mean with ordered poststrata. One approach is to treat poststratum means as random effects, yielding shrinkage towards the unweighted mean, but this method provides unsatisfactory inferences when the means vary systematically across the poststrata. We consider alternative model based extensions of this method, where the poststratum means are assumed to be distributed about a linear regression line, and where the poststratum means are assumed to have an autoregressive covariance structure. The methods are illustrated on a real data set from the Epidemiologic Catchment Area study, and compared with other procedures in a simulation study. The latter suggests that the autoregressive random effects model may be a useful approach to the problem.

Keywords:
Empirical Bayes; random effects; survey inference; superpopulation model; simulation study.