Ideal Point Estimation

by

Royce Carroll

• LAST REVIEWED: 26 May 2023
• LAST MODIFIED: 26 May 2023
• DOI: 10.1093/obo/9780199756223-0360

Introduction

Political scientists have used ideal point estimation primarily to operationalize spatial models of politics, which requires measuring the preferences of actors within a conceptual latent space. Ideal point estimation integrates theoretical ideas from spatial models in economics and political science with measurement theory from psychometrics. Theoretically, the core concept is that a low-dimensional latent preference structure explains behavioral choices or judgments of stimuli. Empirically, the aim is to estimate models of the latent spatial properties of data that can predict an observed set of choice and response data. A central concern of ideal point estimation work in political science has been the generation of meaningful measures of the intervals between the coordinates of actors and the stimuli to which they respond. Accordingly, the primary focus of modern ideal point estimation work has thus been to create empirical spatial models with a theoretical foundation for the estimated locations of actors for use in studies requiring continuous measures of latent preferences. The early development of this work began as part of the study of legislative voting, chiefly among members of the US Congress. This work then extended to other legislative and judicial voting contexts, and eventually to a wide array of different political choice behavior that can be understood through the lens of the spatial models, from speech to social media activity. Related approaches have long been applied to survey data with sophisticated methods to generate measures of actors’ latent preferences, including from multiple data sources. Numerous applications have emerged in the last several decades and continue to grow in number, producing an array of measurement techniques related to ideal point estimation applied to numerous topics in political science, especially political ideology. This bibliography is limited mainly to work focused on or contributing to the literature on the measurement of ideal points, but several applications of ideal point estimation are included due to their influence on this methodological literature.

Spatial Models of Voting Behavior

Numerous studies have attempted to analyze elite voting behavior in settings such as legislatures and courts. Beginning with MacRae 1958 and other early work on US congressional voting, numerous innovations on these approaches have emerged to study the structure and dynamics of legislative voting and judicial decisions, as well as various historical legislative contexts, legislatures outside the United States, and international bodies. In particular, this literature has made significant contributions to topics such as polarization in the US Congress. Interpretations of legislative and judicial voting environments have led to some of the most important innovations in ideal point estimation, such as the influential NOMINATE method from Poole and Rosenthal 1985 and Poole and Rosenthal 1997 and the numerous item response theory (IRT) methods employing Bayesian simulations (notably, Jackman 2001; Martin and Quinn 2002; Clinton, et al. 2004; and Bafumi, et al. 2005), as well as nonparametric methods such as Optimal Classification, introduced in Poole 2000 (see also Rosenthal and Voeten 2004) and various other models (e.g., Heckman and Snyder 1997, Londregan 2000). An array of further innovations have since emerged, such as Lauderdale 2010 and Lewis and Poole 2004 to capture uncertainty; Rosas, et al. 2015 to capture nonresponse; and Carroll, et al. 2013 to incorporate variation in utility functions.

• Bafumi, J., A. Gelman, D. K. Park, and N. Kaplan. “Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation.” Political Analysis 13 (2005): 171–187.

  DOI: 10.1093/pan/mpi010

  Proposes approaches to improving inferences in Bayesian ideal point estimation, such as hierarchical modeling and linear transformations.

• Carroll, R., J. B. Lewis, J. Lo, K. T. Poole, and H. Rosenthal. “The Structure of Utility in Spatial Models of Voting.” American Journal of Political Science 57 (2013): 1008–1028.

  Introduces the alpha-NOMANATE Bayesian ideal point estimation model in which utility functions are a mixture of the quadratic and Gaussian functions.

• Clinton, J., S. Jackman, and D. Rivers. “The Statistical Analysis of Roll Call Data.” American Political Science Review 98 (2004): 355–370.

  DOI: 10.1017/S0003055404001194

  Develops a Bayesian IRT model for ideal point estimation for roll call data. This model has been widely used because of its flexibility in using its parameters to account for various political contexts and for integrating the measurement of ideal points with applications in legislative studies.

• Heckman, J. J., and J. M. Snyder. “Linear Probability Models of the Demand for Attributes with an Empirical Application to Estimating the Preferences of Legislators.” RAND Journal of Economics 28 (1997): S142–S189.

  DOI: 10.2307/3087459

  Presents a linear probability model for ideal point estimation for binary data.

• Jackman, S. “Multidimensional Analysis of Roll Call Data via Bayesian Simulation: Identification, Estimation, Inference, and Model Checking.” Political Analysis 9 (2001): 227–241.

  DOI: 10.1093/polana/9.3.227

  Emphasizes the value of Bayesian methods in enabling the use of vote-specific parameters in higher-dimensional ideal point estimation to help identify the model and incorporate prior beliefs about dimensions.

• Lauderdale, Benjamin E. “Unpredictable Voters in Ideal Point Estimation.” Political Analysis 18.2 (2010): 151–171.

  DOI: 10.1093/pan/mpp038

  Introduces a Bayesian ideal point estimation method based on a heteroskedastic estimator that obtains parameters that capture the degree to which data are not explained by the main dimensions of variance.

• Lewis, Jeffrey B., and Keith T. Poole. “Measuring Bias and Uncertainty in Ideal Point Estimates via the Parametric Bootstrap.” Political Analysis 12.2 (2004): 105–127.

  DOI: 10.1093/pan/mph015

  Introduces an uncertainty measure for the W-NOMINATE model via parametric bootstrap.

• Londregan, J. “Estimating Legislator’s Preferred Points.” Political Analysis 8 (2000): 35–56.

  DOI: 10.1093/oxfordjournals.pan.a029804

  Shows that standard maximum-likelihood estimators result in biased estimates unless the number of choices and individuals is large and proposes a random-effects approach.

• MacRae, Duncan, Jr. Dimensions of Congressional Voting: A Statistical Study of the House of Representatives in the Eighty-First Congress. Berkeley: University of California Press, 1958.

  A pathbreaking study applying methods to understand latent patterns of dimensionality to the US Congress.

• Poole, K. T. “Nonparametric Unfolding of Binary Choice Data.” Political Analysis 8.3 (2000): 211–237.

  DOI: 10.1093/polana/9.3.211

  Introduces the optimal classification method of nonparametric unfolding for binary data based on maximizing the correct classification of votes via a series of cutting planes.

• Poole, K. T., and H. Rosenthal. “A Spatial Model for Legislative Roll Call Analysis.” American Journal of Political Science 29.2 (1985): 357–384.

  DOI: 10.2307/2111172

  Poole and Rosenthal introduce the NOMINATE method for estimating coordinates from observed roll call data using a probabilistic model and a spatial utility function. Introduces the NOMINATE program for one-dimensional analysis with application to roll call voting data for the US House and Senate.

• Rosas, G., Y. Shomer, and S. R. Haptonstahl. “No News Is News: Nonignorable Nonresponse in Roll-Call Data Analysis.” American Journal of Political Science 59 (2015): 511–528.

  DOI: 10.1111/ajps.12148

  Provides an overview of the potential consequences of ignoring nonresponse processes, offering a framework for modeling nonresponse and vote choice.

• Rosenthal, H., and E. Voeten. “Analyzing Roll Calls with Perfect Spatial Voting: France 1946–1958.” American Journal of Political Science 48 (2004): 620–632.

  DOI: 10.1111/j.0092-5853.2004.00091.x

  An application of Poole’s optimal classification method (see Poole 2000) to data from the French Fourth Republic and an overview of the advantages over parametric methods in the context of perfect spatial voting.