Generalized Linear Mixed Models With Crossed Effects and Unit-specific Survey Weights

Mixed models are frequently used in social and economic analysis. Typically, the analyzed data are gathered through a survey sample from the population of interest. The underlying survey design may be non-ignorable, leading to possible bias in the regression parameters if not accounted for. To circumvent this problem, survey weights should be included in the estimation process. We propose a survey weighted generalized linear mixed model allowing for unit-specific survey weights and a flexible random effects structure. An estimation procedure is proposed and evaluated in two simulation studies under different scenarios. The first simulation study strongly encourages the use of survey weighted generalized linear mixed models if the survey design is non-ignorable. The second one replicates a previous simulation study in order to study the competitivity of the proposed method with established approaches and software. Further, the proposed method is used to re-estimate a regression on reading proficiency using US PISA data from 2000. Supplementary files for this article are available online.