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

Abstract

SummaryWe 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.