Multilevel Modeling for the Study of Public Opinion and Voting

这个项目将开发一套通用的工具来理解和检查多层模型的拟合。新的工具包括对非线性、相互作用和方差成分的模型的平均预测效果的计算，以及对多级模型的基于仿真的模型检查的泛化。同时，将探索民意和投票数据的多层次模型。该项目的一个核心应用领域是使用全国民意调查数据来估计不同州的民意时间趋势，这是现有的分别使用州和全国民意调查的方法无法解决的问题。一个相关的工作领域是模拟个体选民之间的依赖结构；也就是说，选民层面的模型可以将地区、州和国家加起来，以预测现实的群体层面的意见模式。这对投票权有影响，也与概率论和社会学中的网络研究有关。预计该项目将在两个方面产生更广泛的影响。首先，多层次模型的诊断方法将广泛涉及社会科学和调查抽样领域的研究人员。其次，民意和投票模式的建模将与州级民意趋势的研究相关（在这个地理极化投票的现代时代，这是一个重要的主题），并有助于理解民意和投票之间的定量关系。

This project will develop a general set of tools for understanding and checking the fit of multilevel models. The new tools include computations of average predictive effects for models with nonlinearity, interactions, and variance components, and generalization of simulation-based model checking for multilevel models. In parallel, multilevel models will be explored for public opinion and voting data. A central application area of this project is to use national poll data to estimate time trends in public opinion for different states, a problem that cannot be solved by existing approaches using state and national polls separately. A related area of work is to model dependence structures among individual voters; that is, voter-level models that can add up districts, states, and the country to predict realistic group-level opinion patterns. This has implications for voting power and also is related to studies of networks in probability theory and sociology.This project is anticipated to have broader impacts in two ways. First, the diagnostic methods for multilevel models will be relevant to a wide range of researchers in social science and survey sampling. Second, the modeling of public opinion and voting patterns will be relevant to studies of state-level opinion trends (an important topic in this modern era of geographically-polarized voting) and for understanding the quantitative relationships between opinion and voting.