Statistical Methods for Multidimensional Scaling and Non- Linear MIMIC Models in Political Science

维度思维是政治讨论的主要内容。记者将政治候选人划分为意识形态光谱的左派或右派。选民们对政客们的评价是离他们近或远。政客们站队，捍卫立场，向某些群体靠拢，远离另一些群体。随着政治事件的展开，政治家、选民和问题经常使用这些几何和空间术语来描述。毫不奇怪，心理学家发现，大多数人，不仅仅是老练的政治分析家，经常用空间和几何术语来概念化和描述社会和政治世界。这为理解投票行为、公众舆论和许多其他形式的政治行为提供了一把钥匙，但要真正有用，我们必须更好地理解当人们说一个政治家接近另一个政治家或他们感觉比另一个更接近一个问题立场时的意思。该项目旨在通过开发统计方法来揭示人们的选择、意见和判断的维度结构，从而更好地了解人们对政治的看法。例如，该项目将开发统计方法和计算机程序，将人们对政治候选人的排名与他们对这些候选人特征的基本观点和信念联系起来。初步研究表明，人们的选择可以用非常少的几个潜在维度来部分解释。在这项研究中开发的方法将能够更清楚地解释为什么这几个维度解释了这么多。这些方法应能使人们更清楚地了解促使选民和其他作出政治选择的人关心的主要问题。此外，由于类似的方法已被广泛应用于理解经济选择，本项目中开发的方法似乎很可能在政治学以外的领域有用。

Dimensional thinking is a mainstay of political discussion. Journalists identify political candidates as on the left or on the right of the ideological spectrum. Voters describe politicians as close to them or far away from them. Politicians take sides, defend positions, move towards some groups, and move away from others. As political events unfold, politicians, voters, and issues are often described by using these kinds of geometric and spatial terms. Not surprisingly, psychologists have found that most people, not just sophisticated political analysts, often conceptualize and describe the social and political world in spatial and geometric terms. This provides a key to understanding voting behavior, public opinion, and many other forms of political behavior, but to be truly useful, we must have a better understanding of what people mean when they say that one politician is close to another or that they feel closer to one issue position than another. This project aims to develop a better understanding of how people think about politics by developing statistical methods for uncovering the dimensional structure of people's choices, opinions, and judgments. For example, the project will develop statistical methods and computer programs for relating peoples' rankings of political candidates to their underlying opinions and beliefs about the characteristics of these candidates. Preliminary research has shown that peoples' choices can be explained partly by a remarkably small number of underlying dimensions. The methods to be developed in this research will enable a clearer interpretation of why this small number of dimensions explains so much. These methods should make it possible to get a clearer understanding of the major concerns which motivate voters and other people who make political choices. In addition, since similar methods have been widely applied to understanding economic choices, it seems likely that the methods developed in this project will be useful in areas outside political science.