An Approximation of Joint Distributions of Weighting Variables Using a Pseudo Population Approach

Abstract

Several weighting techniques require joint distributions of weighting variables on apopulation level in order to adjust for the selectivity in the participation process of the survey. Inpractical applications, joint distributions are frequently not available and population margins arethe only information available to inform the weighting procedure. We propose a novel approachto estimate the population sizes of weighting cells based on a pseudo population that was constructedusing a copula. The approach makes use of population margins of weighting variablesand their correlations. We show how the approach can be used for poststratification and multilevelregression and poststratification approaches and illustrate the usefulness in a simulationstudy and an empirical example. Using the copula pseudo population approach in combinationwith multilevel regression and poststratification for highly selective data strongly improves thesurvey estimation as compared to traditional raking and poststratification methods in our study.