On the Use of Auxiliary Variables in Multilevel Regression and Poststratification.

Area of Science:

• Statistics
• Public Health
• Social Sciences

Background:

• Multilevel regression and poststratification (MRP) is widely used for subgroup estimation, particularly for mitigating selection bias.
• Its effectiveness hinges on strong correlations between auxiliary information and the outcome variable.
• Challenges arise in practical applications, especially with nonprobability survey data.

Purpose of the Study:

• To evaluate the inferential validity of MRP in finite populations.
• To explore the influence of poststratification and model specification on MRP's performance.
• To propose a statistical data integration framework for robust inferences in diverse survey types.

Main Methods:

• Modeling inclusion probabilities conditionally on auxiliary variables.
• Incorporating flexible functions of estimated inclusion probabilities into the mean structure.
• Developing a statistical data integration framework for probability and nonprobability surveys.

Main Results:

• Simulation studies confirm the statistical validity of MRP, demonstrating a bias-variance tradeoff.
• MRP offers significant benefits for subgroup estimates with small sample sizes compared to other methods.
• Application to the Adolescent Brain Cognitive Development (ABCD) Study shows auxiliary variables impact cognitive performance findings.

Conclusions:

• MRP is a statistically valid method for subgroup estimation, particularly beneficial when dealing with small sample sizes and selection bias.
• The proposed data integration framework enhances the fitting performance of outcome models by leveraging auxiliary information.
• Findings from the ABCD Study highlight the critical role of auxiliary variables in understanding cognitive performance in diverse child populations.