Comment: Struggles with Survey Weighting and Regression Modeling

Abstract

This is an intriguing paper that raises important ques tions, and I feel privileged for being invited to discuss it. The paper deals with a very basic problem of sample surveys: how to weight the survey data in order to esti mate finite population quantities of interest like means, differences of means or regression coefficients. The paper focuses for the most part on the com mon estimator of a population mean, yw = Xw=i wiyil YTi= wi, and discusses different approaches to con structing the weights by use of linear regression mod els. These models vary in terms of the number and na ture of the regressors in the model and in the assump tions regarding the regression coefficients, whether fixed or random with prespecified distributions. The idea behind regression weighting is to include in the regression model all the variables and interactions that are related to the outcome values and affect the sam ple selection and the response probabilities, such that the sampling and response mechanisms are ignorable in the sense that the model fitted to the observed data is