Bayesian Multilevel Estimation with Poststratification: State-Level Estimates from National Polls

Abstract

We fit a multilevel logistic regression model for the mean of a binary response variable conditional on poststratification cells. This approach combines the modeling approach often used in small-area estimation with the population information used in poststratification (see Gelman and Little 1997, Survey Methodology 23:127-135). To validate the method, we apply it to U.S. preelection polls for 1988 and 1992, poststratified by state, region, and the usual demographic variables. We evaluate the model by comparing it to state-level election outcomes. The multilevel model outperforms more commonly used models in political science. We envision the most important usage of this method to be not forecasting elections but estimating public opinion on a variety of issues at the state level.

How Does Multilevel Regression and Poststratification Perform with Conventional National Surveys?

“…MRP has the potential to unlock these possibilities. Relying on the work of Gelman and Little (1997) that was extended in Park, Gelman, andBafumi (2004, 2006), Lax and Phillips (2009b) and Warshaw and Rodden (2012) take MRP into a different survey context-one where sample sizes are much smaller-and find instances where the performance of MRP remains strong. Although we agree that its performance exceeds that of other methods and that the margin of overperformance is greatest with smaller sample sizes, we also find substantial variation in how well MRP performs.…”

The Democratic Effect of Direct Democracy

“…To derive preference measures, we conducted two surveys asking cantonal politicians and voters whether they support a total of 10 tax, healthcare, education, and family policies. With this data and fine-grained census information, we estimate elite and voter preference measures, as well as the deviations between the two, using multilevel modeling and post-stratification (Gelman and Little, 1997;Park et al, 2004). This study makes a substantial contribution to the literature on direct democracy by providing an empirical investigation that relies on consistent measures of policy congruence and accurate estimates of the preferences of the electorate and the political elite over various policy areas.…”

Comparing Strategies for Estimating Constituency Opinion from National Survey Samples

“…Initial studies mapped the relative benefits of certain elements of MRP in the context of estimating opinion for the 50 US states (Park, Gelman and Bafumi 2004;Lax and Phillips 2009). …”

“…In contrast, for any demographic variable that has L k > 2 levels (i.e. age, edu, and socgrd), the α k terms for that variable are modeled as draws from a common prior distribution which is normal with mean 0 and estimated variance (Park, Gelman and Bafumi 2004).…”