Doubly-robust weight smoothing models to smooth post-stratification weights in case of a Gaussian survey outcome

Abstract

In order to obtain unbiased estimates of a population quantity based on sample survey data, post-stratification techniques use external data to adjust the estimates during the analysis stage. Small sample sizes in any post- strata may yield highly variable estimator. The weight trimming method pools highly underrepresented units into a stratum with better representation but it is somehow arbitrary. In the same spirit, weight-smoothing approach treats post-stratum means as random-effects, inducing shrinkage across post-stratum means. To protect against the bias generated by possible misspecification of the mixed-model, a doubly-robust version is used as well as a nonparametric spline function for the underlying weight stratum means. I compare those approaches in a simulation study for the inference about the population mean of a normally distributed survey outcome with ordinal post-stratifying variable. None of the 9 estimators is uniformly best in all 24 scenarios considered but the nonparametric weight-smoothing doubly-robust is close to the best for a wide range of populations offering protection against unfavorable mean structures and model misspecification, therefore can be seen as a robust technique. The methods are illustrated by estimating the weekly working hours using data from the 2008 Quality of Life Survey in Colombia.