Post-Stratification: A Modeler's Perspective

Abstract Post-stratification is a common technique in survey analysis for incorporating population distributions of variables into survey estimates. The basic technique divides the sample into post-strata, and computes a post-stratification weight w ih = rP h /r h for each sample case in post-stratum h, where r h is the number of survey respondents in post-stratum h, P h is the population proportion from a census, and r is the respondent sample size. Survey estimates, such as functions of means and totals, then weight cases by w h . Variants and extensions of the method include truncation of the weights to avoid excessive variability and raking to a set of two or more univariate marginal distributions. Literature on post-stratification is limited and has mainly taken the randomization (or design-based) perspective, where inference is based on the sampling distribution with population values held fixed. This article develops Bayesian model-based theory for the method. A basic normal post-stratification mod...