Self-selected samples are frequently obtained due to different levels of survey participation propensity of the survey individuals. When the survey participation is related to the survey topic of interest, propensity score weighting adjustment using auxiliary information may lead to biased estimation. In this paper, we consider a parametric model for the response probability that includes the study variable itself in the covariates of the model and proposes a novel application of two-phase sampling to estimate the parameters of the propensity model. The proposed method includes an experiment in which data are collected again from a subset of the original self-selected sample. With this two-phase sampling experiment, we can estimate the parameters in a propensity score model consistently. Then the propensity score adjustment can be applied to the self-selected sample to estimate the population parameters. Sensitivity of the selection model assumption is investigated from two limited simulation studies. The proposed method is applied to the 2012 Iowa Caucus Survey.
"Two-phase sampling experiment for propensity score estimation in self-selected samples." Ann. Appl. Stat. 8 (3) 1492 - 1515, September 2014. https://doi.org/10.1214/14-AOAS746