Estimating Ideal Points from Roll-Call Data: Explore Principal Components Analysis, Especially for More Than One Dimension?

Abstract

Abstract:For two or more dimensions, the two main approaches to estimating legislators' ideal points from roll-call data entail arbitrary, yet consequential, identification and modeling assumptions that bring about both indeterminateness and undue constraints for the ideal points. This paper presents a simple and fast approach to estimating ideal points in multiple dimensions that is not marred by those issues. The leading approach at present is that of Poole and Rosenthal. Also prominent currently is one that uses Bayesian techniques. However, in more than one dimension, they both have several problems, of which nonidentifiability of ideal points is the most precarious. The approach that we offer uses a particular mode of principal components analysis to estimate ideal points. It applies logistic regression to estimate roll-call parameters. It has a special feature that provides some guidance for deciding how many dimensions to use. Although its relative simplicity makes it useful even in just one dimension, its main advantages are for more than one.

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