  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.
