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

Richard Potthoff

doi:10.3390/socsci7010012

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.

Highlights

The use of roll-call data to place the positions of legislators within a political or ideological spectrum or space is common, in academic research and, to some degree, in mainstream media and in relation to political campaigns
Our PCA approach to estimating ideal points from roll-call data is simple in both concept and implementation, and its computation is fast
For analysis of roll-call data, this paper builds a case for considering our PCA approach as an alternative to P-R and CJR, two well-established methods

Summary

Introduction

The use of roll-call data to place the positions of legislators within a political or ideological spectrum or space is common, in academic research and, to some degree, in mainstream media and in relation to political campaigns. One may alternatively refer to these spatial positions as locations, or scores, or ideal points. In the bulk of applications, the space is one-dimensional, with the single dimension interpreted in terms of a spectrum of “left”-“right” or “liberal”-“conservative” political ideology. Space with two or more dimensions is of potential importance beyond the limited attention it has yet received, as will be covered in Section 2 below. Ideal-point estimates can have different origins and different applications. Use of results from the Poole-Rosenthal approach has predominated, though certain Bayesian methodology has become available more recently.

Results

Discussion

Conclusion