Evidence Pack: How Multilevel Regression and Poststratification (MRP) Estimates Local Opinion from National Polls

In 2012, when the Pew Research Center attempted to estimate the voting behavior of Hispanic Americans using a standard opt-in online poll, the traditional weighting method known as raking produced a margin of error of plus or minus 7 percentage points. That wide interval made it difficult to draw precise conclusions about the subgroup. However, when statisticians ran the exact same raw survey data through a technique called Multilevel Regression and Poststratification (MRP), the margin of error shrank to just plus or minus 4 points. The national-level accuracy remained identical at plus or minus 2 points, but the subgroup precision nearly doubled.[1]

This mathematical leverage is why MRP—often affectionately called "Mister P" by statisticians—has become the gold standard for modern public opinion research. As response rates for traditional random-digit dialing have plummeted below 5 percent, pollsters have increasingly relied on large, non-representative online panels. Extracting a meaningful signal from these skewed samples requires aggressive statistical correction.

"Traditional polling methods often struggled with accurately representing small or niche groups within larger populations," notes the Australian research firm DemosAU. This limitation forced researchers to either ignore local trends or spend millions fielding massive, localized surveys. MRP bypasses this barrier by mathematically decoupling the survey sample from the population structure.

The methodology solves the non-representative sample problem in two distinct steps, beginning with multilevel regression. Instead of simply averaging the responses of the people who happened to take the survey, the model treats the data as a hierarchical structure. It estimates how various demographic traits—such as age, gender, education, and geographic location—interact to predict an individual's response.[2]

Crucially, this regression step employs a Bayesian technique known as "partial pooling." If a survey only captures a handful of young Hispanic voters in Ohio, traditional cross-tabulations would yield a highly volatile estimate for that specific group. MRP, however, allows that sparse cell to borrow statistical strength from young voters nationally, Hispanic voters in neighboring states, and Ohioans overall.[3]

This smoothing prevents small sample sizes from producing wild, noisy outliers. As the Pew Research Center explains, "The main advantage of MRP is that it lets researchers perform these kinds of complex adjustments without the same penalty to precision." The model learns the underlying relationships between demographics and opinions, rather than relying on raw headcounts.[1]

The second step is poststratification. Once the regression model has predicted the likely opinion of every possible demographic combination—often creating thousands of distinct "cells"—the algorithm weights each cell by its actual frequency in the true target population.

If official Census data shows that 35-year-old college-educated women make up exactly 1.2 percent of a state's population, their predicted opinion is weighted at exactly 1.2 percent of the final state estimate. This rigid recalibration occurs regardless of whether that demographic made up 5 percent of the survey sample or 0.1 percent.

The result is a synthetic but highly accurate projection of public opinion. By mapping modeled preferences onto rigid demographic benchmarks, MRP allows researchers to generate reliable state-by-state or district-by-district estimates from a single national survey.[3]

The technique gained mainstream fame in the United Kingdom when the polling firm YouGov used it to correctly predict the outcome in 93 percent of parliamentary constituencies during the 2017 general election. In the United States, researchers use MRP to estimate local health outcomes, combining survey data with demographic benchmarks to map disease prevalence at the census-tract level.[2][3]

However, the methodology comes with strict mathematical trade-offs. The most significant limitation is computational cost. Because MRP builds a predictive model for the outcome itself, researchers must run a separate, computationally intensive regression for every single question on a survey.[1]

Traditional raking, by contrast, calculates a single weight for each respondent that can be applied across a 40-question survey instantly. "If you have a survey with 40 questions, you would need to run MRP 40 times," the Pew Research Center noted, citing practicality as the primary barrier to universal adoption.[1]

Furthermore, MRP is entirely dependent on the quality of its poststratification frame. If the underlying Census data is outdated, or if the model omits a variable that strongly drives opinion—such as political party registration—the poststratification step will confidently project a biased result. The model can only correct for the demographic skews it is explicitly told to measure.[3]

Despite these constraints, the variance reduction MRP offers is transforming how polling organizations handle sparse data. By mathematically rebuilding the population from the ground up, statisticians at firms like YouGov and Pew can now extract high-resolution, localized insights from the noisy, fragmented reality of modern polling.[4]