Title: Multivariate MRP Show Chinese title

Title: 多变量MRP

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. Show Chinese abstract

Abstract: 在次国家地理范围内测量公众意见对于政治科学中的许多理论至关重要。多级回归和后分层（MRP）是一种常用的工具，尽管现有工作仅限于测量单一调查问题的意见。我们提供了一个框架，用于估计多个问题意见的联合分布（“多元MRP”）。为此，我们推导了一种在具有许多随机效应的多项逻辑回归中进行变分推断的新方法。这需要在高维固定效应下进行变分推 inference，但我们证明这可以在较低的计算成本下完成。我们通过在美国按政党估算公众意见来验证此过程，并表明通过在政党认同的先验水平上添加上下文协变量，可以显著改进现有方法。从实质上看，我们展示了多元MRP的输出如何用于同时研究多个政策议题上的代表性。