Skip to main content Accessibility help

BARP: Improving Mister P Using Bayesian Additive Regression Trees



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.


Corresponding author

*James Bisbee, PhD Candidate, NYU Wilf Family Department of Politics, New York University,


Hide All

I am grateful to Neal Beck, Patrick Egan, Shane Mahon, Keith McCart, Kevin Munger, Thiago Moreira da Silva, and Drew Dimmery for their helpful feedback. Replication files are available at the American Political Science Review Dataverse:



Hide All
Bartels, Larry M. 1991. “Constituency Opinion and Congressional Policy Making: The Reagan Defense Buildup.” American Political Science Review 85 (2): 457–74.
Buttice, Matthew K., and Highton, Benjamin. 2013. “How Does Multilevel Regression and Poststratification Perform with Conventional National Surveys?Political Analysis 21 (4): 449–67.
Caughey, Devin, and Warshaw, Christopher. 2019. “Public Opinion in Subnational Politics.” The Journal of Politics 81 (1): 352–63. URL:
Chipman, Hugh A., George, Edward I., and McCulloch, Robert E.. 2010. “BART: Bayesian Additive Regression Trees.” The Annals of Applied Statistics 4 (1): 266–98.
Gelman, Andrew. 2013. “Last Word on Mister P (For Now).” URL:
Gelman, Andrew. 2018. “Regularized Prediction and Poststratification (The Generalization of Mister P).” URL:
Gelman, Andrew, and Little, Thomas C.. 1997. “Poststratification into many Categories Using Hierarchical Logistic Regression.” Survey Methodology 23 (2): 127–35.
Ghitza, Yair, and Gelman, Andrew. 2013. “Deep Interactions with MRP: Election Turnout and Voting Patterns Among Small Electoral Subgroups.” American Journal of Political Science 57 (3): 762–76.
Hanretty, Chris, Lauderdale, Benjamin E., and Vivyan, Nick. 2018. “Comparing Strategies for Estimating Constituency Opinion from National Survey Samples.” Political Science Research and Methods 6 (3): 571–91.
Hare, Christopher, and Monogan, James E.. 2018. “The Democratic Deficit on Salient Issues: Immigration and Healthcare in the States.” Journal of Public Policy: 1–28. Published online 22 October 2018.
Kapelner, Adam, and Bleich, Justin. 2013. “bartMachine: Machine Learning with Bayesian Additive Regression Trees.” arXiv preprint arXiv:1312.2171.
Lax, Jeffrey R., and Phillips, Justin H.. 2009. “How Should We Estimate Public Opinion in the States?American Journal of Political Science 53 (1): 107–21.
Lax, Jeffrey R., and Phillips, Justin H.. 2012. “The Democratic Deficit in the States.” American Journal of Political Science 56 (1): 148–66.
Linero, Antonio R. 2017. “A Review of Tree-Based Bayesian Methods.” Communications for Statistical Applications and Methods 24 (6): 543–59.
Polley, Eric C., and Van der Laan, Mark J.. 2015. SuperLearner: Super Learner Prediction. (Package Version 2.0-15). Vienna, Austria: R Foundation for Statistical Computing.
Trangucci, Rob, Ali, Imad, Gelman, Andrew, and Rivers, Doug. 2018. “Voting Patterns in 2016: Exploration Using Multilevel Regression and Poststratification (MRP) on Pre-election Polls.” arXiv preprint arXiv:1802.00842.
Warshaw, Christopher, and Rodden, Jonathan. 2012. “How Should We Measure District-Level Public Opinion on Individual Issues?The Journal of Politics 74 (1): 203–19.
Type Description Title
Supplementary materials

Bisbee Dataset

Supplementary materials

Bisbee supplementary material
Bisbee supplementary material 1

 PDF (960 KB)
960 KB

BARP: Improving Mister P Using Bayesian Additive Regression Trees



Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed