Multivariate MRP

TL;DR

This paper introduces a multivariate extension of MRP, enabling joint estimation of opinions on multiple questions, with a novel variational inference method for high-dimensional multinomial logistic models, validated on US political data.

Contribution

It develops a new framework for multivariate MRP and a low-cost variational inference technique for complex models, enhancing analysis of multiple opinion dimensions.

Findings

Improved estimation of public opinion across multiple issues.

Adding contextual covariates enhances model accuracy.

Demonstrated applicability to US political opinion data.

Abstract

Measuring public opinion at subnational geographies is critical to many theories in political science. Multilevel regression and post-stratification (MRP) is a popular tool for doing so, although existing work is limited to measuring opinion on a single survey question. We provide a framework for estimating the joint distribution of opinion on multiple questions ("Multivariate MRP"). To do so, we derive a novel method for variational inference in multinomial logistic regression with many random effects. This requires performing variational inference with high-dimensional fixed effects, but we show that this can be done at a low computational cost. We validate this procedure by estimating public opinion by party in the United States and show that existing methods can be improved considerably by adding contextual covariates on the prior levels of party identification. Substantively, we show how the output of multivariate MRP can be used to study representation across multiple policy issues simultaneously.