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Multilevel regression and poststratification (MRP) is a popular method foraddressing selection bias in subgroup estimation, with broad applicationsacross fields from social sciences to public health. In this paper, we examinethe inferential validity of MRP in finite populations, exploring the impact ofpoststratification and model specification. The success of MRP relies heavilyon the availability of auxiliary information that is strongly related to theoutcome. To enhance the fitting performance of the outcome model, we recommendmodeling the inclusion probabilities conditionally on auxiliary variables andincorporating flexible functions of estimated inclusion probabilities aspredictors in the mean structure. We present a statistical data integrationframework that offers robust inferences for probability and nonprobabilitysurveys, addressing various challenges in practical applications. Oursimulation studies indicate the statistical validity of MRP, which involves atradeoff between bias and variance, with greater benefits for subgroupestimates with small sample sizes, compared to alternative methods. We haveapplied our methods to the Adolescent Brain Cognitive Development (ABCD) Study,which collected information on children across 21 geographic locations in theU.S. to provide national representation, but is subject to selection bias as anonprobability sample. We focus on the cognition measure of diverse groups ofchildren in the ABCD study and show that the use of auxiliary variables affectsthe findings on cognitive performance.

On the Use of Auxiliary Variables in Multilevel Regression and Poststratification