Are Survey Weights Necessary? the Maximum Likelihood Approach to Sample Survey Inference

In the present work we explicate the application of maximum likelihood inference in the analysis of surveys which are the result of (possibly informative) stratified sampling. In Section 1 we review basic ideas, including two general results useful for applying maximum likelihood to sample data. Ideas are illustrated by a simple through the origin regression model. In Section 2, we discuss the application of these ideas to the situation of (possibly) informative stratified sampling. The variable of interest Y depends linearly on covariates x, and the stratification variable T depends linearly on x and Y. For simplicity, we focus on the through the origin model, taking T = Y. Section 3 gives results of a simulation study, and Section 4 states conclusions.