A Brief Review of Approaches to Non-ignorable Non-response

While there exist numerous methods to handle ignorable non-response, the literature on non-ignorable non-response is somewhat sparse. In this article, we review the main approaches to imputation for missing data and to parameter estimation in the presence of missing data. We focus almost exclusively on the methods applicable to situations where non-response is not missing at random, such that the probability to respond depends on the variables that are missing. In this case, the non-response cannot be ignored. We discuss item non-response, where the missingness occurs only in the outcome variable, while the auxiliary (explanatory) variables are observed for both respondents and non-respondents, as well as unit non-response, where neither the outcome variable nor the covariates of the non-respondents are observed. We also illustrate an application of some of the methods described and compare their performance using a real data set.