Likelihood-Based Inference for the Finite Population Mean with Post-Stratification Information Under Non-Ignorable Non-Response

We describe models and likelihood-based estimation of the finite population mean for a survey subject to unit non-response, when post-stratification information is available from external sources. A feature of the models is that they do not require the assumption that the data are missing at random (MAR). As a result, the proposed models provide estimates under weaker assumptions than those required in the absence of post-stratification information, thus allowing more robust inferences. In particular, we describe models for estimation of the finite population mean of a survey outcome with categorical covariates and externally observed categorical post-stratifiers. We compare inferences from the proposed method with existing design-based estimators via simulations. We apply our methods to school-level data from California Department of Education to estimate the mean academic performance index (API) score in years 1999 and 2000. We end with a discussion.