Likelihood-based inference for the finite population mean with post-stratification information under nonignorable nonresponse

Abstract

We describe models and likelihood-based estimation of the nite population mean
for a survey subject to unit nonresponse, when post-stratication information is avail-
able from external sources. A feature of the models is that they do not require the assumption that the data are missing at random (MAR), or specific models for the missingness mechanism. As a result, the proposed models provide estimates under weaker assumptions than those required in the absence of post-stratication 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-stratiers. We compare inferences from the proposed method with existing design-based estimators via simulations. We apply our methods to school-level data from the California Department of Education to estimate the mean academic performance index (API) score in years 1999 and 2000. We end with a discussion.