Many conventional ideal point estimation techniques are inappropriate when only a limited number of votes are available. This paper presents a covariate-based random-effects Bayesian approach that allows scholars to estimate ideal points based on fewer votes than required for fixed-effects models. Using covariates brings more information to bear on the estimation; using a Bayesian random-effects approach avoids incidental parameter problems. Among other things, the method allows us to estimate directly the effect of covariates such as party on preferences and to estimate standard errors for ideal points. Monte Carlo results, an empirical application, and a discussion of further applications demonstrate the usefulness of the method.

The purpose of this paper is to show how the geometry of the quadratic utility function in the standard spatial model of choice can be exploited to estimate a model of parliamentary roll call voting. In a standard spatial model of parliamentary roll call voting, the legislator votes for the policy outcome corresponding to Yea if her utility for Yea is greater than her utility for Nay. The voting decision of the legislator is modeled as a function of the difference between these two utilities. With quadratic utility, this difference has a simple geometric interpretation that can be exploited to estimate legislator ideal points and roll call parameters in a standard framework where the stochastic portion of the utility function is normally distributed. The geometry is almost identical to that used by Poole (2000) to develop a nonparametric unfolding of binary choice data and the algorithms developed by Poole (2000) can be easily modified to implement the standard maximum-likelihood model.

Vote-specific parameters are often by-products of roll call analysis, the primary goal being the measurement of legislators' ideal points. But these vote-specific parameters are more important in higher-dimensional settings: prior restrictions on vote parameters help identify the model, and researchers often have prior beliefs about the nature of the dimensions underlying the proposal space. Bayesian methods provide a straightforward and rigorous way for incorporating these prior beliefs into roll call analysis. I demonstrate this by exploiting the close connections among roll call analysis, item-response models, and “full-information” factor analysis. Vote-specific discrimination parameters are equivalent to factor loadings, and as in factor analysis, they (1) enable researchers to discern the substantive content of the recovered dimensions, (2) can be used for assessing dimensionality and model checking, and (3) are an obvious vehicle for introducing and testing researchers' prior beliefs about the dimensions. Bayesian simulation facilitates these uses of discrimination parameters, by simplifying estimation and inference for the massive number of parameters generated by roll call analysis.

Existing preference estimation procedures do not incorporate the full structure of the spatial model of voting, as they fail to use the sequential nature of the agenda. In the maximum likelihood framework, the consequences of this omission may be far-reaching. First, information useful for the identification of the model is neglected. Specifically, information that identifies the proposal locations is ignored. Second, the dimensionality of the policy space may be incorrectly estimated. Third, preference and proposal location estimates are incorrect and difficult to interpret in terms of the spatial model. We also show that the Bayesian simulation approach to ideal point estimation (Clinton et al. 2000; Jackman 2000) may be improved through the use of information about the legislative agenda. This point is illustrated by comparing several preference estimators of the first U.S. House (1789–1791).

This article uses spatial voting theory to analyze the properties of linear regressions that employ interest group ratings as measures of legislator policy preferences. Such regressions, in general, yield inconsistent results. In particular, least-squares estimation of a bivariate regression which contains an interest group rating as a regressor produces an inflated slope estimate. Instrumenting for the rating with a second rating, as proposed by Brunell et al. (1999), does not fix this problem, and this is because errors in both sets of ratings are correlated. Finally, estimation of a trivariate regression that contains an interest group rating and a party indicator on its right-hand side yields inconsistent slope estimates and, in particular, a party coefficient estimate of unreliable sign. Hence, regressions including both ratings and party indicators are not useful tools in the debate on whether party affiliation has an independent impact on legislator behavior.

This paper presents a method for inferring the distribution of voter ideal points on a single dimension from individual-level binary choice data. The statistical model and estimation technique draw heavily on the psychometric literature on test taking and, in particular, on the work of Bock and Aitkin (1981) and are similar to several recent methods of estimating legislative ideal points (Londregan 2000; Bailey 2001). I present Monte Carlo results validating the method. The method is then applied to determining the partisan and ideological basis of support for presidential candidates in 1992 and to U.S. mass and congressional partisan realignment on abortion policy since 1973.