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Properties of Ideal-Point Estimators Tahk, Alexander Uploaded 07-20-2010 Keywords ideal points ideal-point estimation consistency Quinn conjecture optimal classification Abstract Although ideal-point estimation has become relatively commonplace in political science, fairly little is known about the properties of these estimations. Two of the most common estimators—NOMINATE and the Bayesian approach of Clinton, Jackman, and Rivers—suffer from the incidental parameters problem, implying that standard results about the consistency of maximum-likelihood and Bayes estimators do not apply. Thus, despite their widespread use, these estimators are not known to be consistent and may lead to erroneous results even in very large samples. This paper provides several theoretical results regarding ideal-point estimation. First, this paper demonstrates a counterexample to consistency of common ideal-point estimators—even with regard to the rank of the ideal points. It then presents a simple estimator of the rank of unidimensional ideal points that is inefficient but also consistent for a generalization of most common ideal-point models.

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The Most Liberal Senator: Analyzing and Interpreting Congressional Roll Calls Clinton, Joshua Jackman, Simon Rivers, Doug Uploaded 05-12-2004 Keywords ideal points roll call voting 2004 presidential election Abstract The non-partisan National Journal recently declared Senator John Kerry to be the "top liberal" in the Senate based on analysis of 62 roll calls in 2003. Although widely reported in the media (and the subject of a debate among the Democratic presidential candidates), we argue that this characterization of Kerry is misleading in at least two respects. First, when we account for the "margin of error: in the voting scores -- which is considerable for Kerry given that he missed 60% of the National Journal's key votes while campaigning -- we discover that the probability that Kerry is the "top liberal" is only .30, and that we cannot reject the conclusion that Kerry is only the 20th most liberal senator. Second, we compare the position of the President Bush on these key votes; including the President's announced positions on these votes reveals the President to be just as conservative as Kerry is liberal (i.e., both candidates are extreme relative to the 108th Senate). A similar conclusion holds when we replicate the analysis using all votes cast in the 107th Senate. A more comprehensive analysis than that undertaken by National Journal (including an accounting of the margins of error in voting scores) shows although Kerry belongs to the most liberal quintile of the contemporary Senate, Bush belongs to the most conservative quintile.

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Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation Bafumi, Joseph Gelman, Andrew Park, David K. Kaplan, Noah Uploaded 06-11-2004 Keywords Ideal points Bayesian Logistic regression Rasch model Abstract In recent years, logistic regression (Rasch) models have been used in political science for estimating ideal points of legislators and Supreme Court justices. These models present estimation and identifiability challenges, such as improper variance estimates, scale and translation invariance, reflection invariance, and issues with outliers. We resolve these issues using Bayesian hierarchical modeling, linear transformations, informative regression predictors, and explicit modeling for outliers. In addition, we explore new ways to usefully display inferences and check model fit.

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A Note Relating Ideal Point Estimates to the Spatial Model Clinton, Joshua Meirowitz, Adam Uploaded 07-18-2000 Keywords ideal points preference estimation NOMINATE spatial model Abstract Existing preference estimators do not incorporate the full structure of the spatial model. Specifically, they fail to use the sequential nature of the agenda by not constraining the nay location of a bill to be the yea location of the last successful policy. The consequences of this omission may be far-reaching. Not only is information useful for the identification of the model neglected, but more seriously, the dimensionality of the policy space may be incorrectly estimated. Preference and bill location estimates are uninterpretable in terms of the spatial model. We show that under very general assumptions, ML estimates of ideal points that do not constrain the nay locations will differ from ML estimates that constrain the nay locatios -- a difference that does not vanish as the numbers of votes goes to infinity. Additionally, unconstrained models underestimate the true dimensionality of the policy space. We derive a Maximum Likelihood estimator of legislative preferences and bill locations that shares basic assumptions with the spatial model of voting.

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A Random Effects Approach to Legislative Ideal Point Estimation Bailey, Michael Uploaded 04-21-1998 Keywords ideal points random effects models Bayesian estimation em algorithm Abstract Conventionally, scholars use either standard probit/logit techniques or fixed-effect methods to estimate legislative ideal points. However, these methods are unsatisfactory when a limited number of votes are available: standard probit/logit methods are poorly equipped to handle multiple votes and fixed-effect models disregard serious ``incidental parameter'' problems. In this paper I present an alternative approach that moves beyond single-vote probit/logit analysis without requiring the large number of votes needed for fixed-effects models. The method is based on a random effects, panel logit framework that models ideal points as stochastic functions of legislator characteristics. Monte Carlo results and an application to trade politics demonstrate the practical usefulness of the method.

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Scaling the Critics: Uncovering the Latent Dimensions of Movie Criticism with An Item Response Approach Peress, Michael Spirling, Arthur Uploaded 07-04-2008 Keywords threshold utility model film ideal points Abstract We study the critical opinions of expert movie reviewers as an item response problem. We develop a framework that models an individual's decision to approve or disapprove of an item. Using this framework, we are able to recover the locations of movies and ideal points of critics in the same multi-dimensional space. We demonstrate that a three dimensional model captures much of the variation in critical opinions. The first dimension signifies movie 'quality' while the other two connote the nature and subject matter of the films. We then demonstrate that the dimensions uncovered from our 'threshold utility model' are statistically significant predictors of a movie's success, and are particularly useful in predicting the success of `independent' films.