On the Use of Auxiliary Variables in Multilevel Regression and Poststratification

Multilevel regression and poststratification (MRP) has been a popular approach for selection bias adjustment and subgroup estimation, with successful and widespread applications from social sciences to health sciences. We demonstrate the capability of MRP to handle the methodological and computational issues in data integration and inferences of probability and nonprobability-based surveys, and the broad extensions in practical applications. Our development is motivated by the Adolescent Brain Cognitive Development (ABCD) Study that has collected children across 21 U.S. geographic locations for national representation but is subject to selection bias, a common problem of nonprobability samples. Though treated as the gold standard in public opinion research, MRP is a statistical technique that has assumptions and pitfalls, the validity of which prominently depends on the quality of available auxiliary information. In this paper, we develop the statistical foundation of how to incorporate auxiliary variables under MRP. We build up a systematic framework under MRP for statistical data integration and inferences. Our simulation studies indicate the statistical validity of MRP with a tradeoff between robustness and efficiency and present the improvement over alternative methods. We apply the approach to evaluate cognition performances of diverse groups of children in the ABCD study and find that the adjustment of auxiliary variables has a substantial effect on the inference results.