Say I have a target population of 10,000 for a survey, and only 2,000 respond, because they likely feel strongly about the survey topic (either happy or angry). I have clear, abundant non-response bias.
Say one of the questions is to rate something from 1-5, let's call this random variable $y$. How can I best adjust for non-response bias in estimating the population mean $\hat{\overline{y}}_{pop}$? I am hoping to obtain auxiliary variables, such as age, for both the respondents and non-respondents.
I don't think I want to use weighting-class adjustment because I don't have missing at random. I am trying to figure out a way to use propensity score weights and/or regression, if possible, but am not quite connecting the dots. Could anyone help me out?
