Embedded Multilevel Regression and Poststratification: Model-based Inference with Incomplete Auxiliary Information

Health disparity research often evaluates health outcomes across subgroups. Multilevel regression and poststratification (MRP) is a popular approach for small subgroup estimation due to its ability to stabilize estimates by fitting multilevel models and to adjust for selection bias by poststratifying on auxiliary variables, which are population characteristics predictive of the analytic outcome. However, the granularity and quality of the estimates produced by MRP are limited by the availability of the auxiliary variables' joint distribution; data analysts often only have access to the marginal distributions. To overcome this limitation, we develop an integrative inference framework that embeds the estimation of population cell counts needed for poststratification into the MRP workflow: embedded MRP (EMRP). Under EMRP, we generate synthetic populations of the auxiliary variables before implementing MRP. All sources of estimation uncertainty are propagated with a fully Bayesian framework. Through simulation studies, we compare different methods and demonstrate EMRP's improvements over classical MRP on the bias-variance tradeoff to yield valid subpopulation inferences of interest. As an illustration, we estimate food insecurity prevalence among vulnerable groups in New York City by applying EMRP to the Longitudinal Survey of Wellbeing. We find that the improvement is primarily on subgroup estimation with efficiency gains.