RandomEffects 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.
