BARP: Improving Mister P Using Bayesian Additive Regression Trees

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Abstract
Multilevel regression and post-stratification (MRP) is the current gold standard for extrapolating opinion data from nationally representative surveys to smaller geographic units. However, innovations in nonparametric regularization methods can further improve the researcher’s ability to extrapolate opinion data to a geographic unit of interest. I test an ensemble of regularization algorithms and find that there is room for substantial improvement on the multilevel model via more flexible methods of regularization. I propose a modified version of MRP that replaces the multilevel model with a nonparametric approach called Bayesian additive regression trees (BART or, when combined with post-stratification, BARP). I compare both methods across a number of data contexts, demonstrating the benefits of applying more powerful regularization methods to extrapolate opinion data to target geographical units. I provide an R package that implements the BARP method.

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