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The Past and Future of Ideal Point Estimation

Remarks Delivered at the Ideal Point Estimation Conference
Washington University, St. Louis, 20 September 2002

Revised For EITM Summer Institute, 20 June 2006

Keith T. Poole

"The Evolving Influence of Psychometrics in Political Science," Oxford Handbook of Political Methodology, edited by Jan Box-Steffensmeier, Henry Brady, and David Collier. New York: Oxford University Press (forthcoming).


  1. A Short History of Ideal Point Estimation

    1. Introduction

    2. Karl Pearson

      1. Principal Components Analysis

    3. Charles Spearman

      1. Spearman Correlation Matrix

    4. L. L. Thurstone

    5. Harold Hotelling

    6. Carl H. Eckart

      1. The Eckart-Young Theorem (Singular Value Decomposition and Lower-Rank Approximation)

      2. Singular Values and the Dispersion of Data

    7. Warren S. Torgerson

      1. Small Example of Double-Centering Using Roll Call Data

      2. Agreement Scores for 88th Senate

      3. Eigenvalues of Double-Centered Agreement Score Matrix for 88th Senate

      4. Plot of First Two Eigenvectors for 88th Senate

      5. Eigenvalues of Double-Centered Agreement Score Matrix for 106th House and Senate

      6. Plot of First Two Weighted and Unweighted Eigenvectors of Double-Centered Agreement Score Matrix for 107th Senate

    8. Clyde H. Coombs

      1. I and J Scales

      2. Feeling Thermometers as an Unfolding Problem

      3. Roll Call Votes as an Unfolding Problem

        Measurement Theory: Homework 5

        Measurement Theory: Homework 8

        Measurement Theory: Homework 9

        Measurement Theory: Homework 12

    9. Roger N. Shepard and Joseph B. Kruskal

      1. The Morse Code Data

      2. Two Dimensional Configuration of The Morse Code Data

      3. Shepard Diagram for The Morse Code Data

      4. Stress Plots for Morse Code and Color Data

      5. The Color Data

      6. Shepard Diagram for The Color Data

      7. The Color Circle

    10. Duncan MacRae

      1. Duncan MacRae's Analysis of the 87th House

    11. Herbert F. Weisberg and George Rabinowitz

      1. Non-Metric MDS Applied to the 1968 Feeling Thermometers

  2. The NOMINATE Model

    1. The Framework

      1. The Spatial Theory of Melvin J. Hinich and Peter C. Ordeshook

      2. The Random Utility Model

        1. The Deterministic Utility Function

        2. The Error Distribution

      3. Alternating Estimation Method From Psychometrics

    2. Basic Geometry of the Roll Call Voting Problem

      1. Geometry of a Roll Call Vote

      2. Geometry of a Legislator Ideal "Point"

    3. Design Issues Encountered in the Development of NOMINATE

      1. The "Sag" Problem

      2. The Unit Hypersphere Constraints on Legislators and Roll Calls

    4. NOMINATE: Nominal-Three-Step-Estimation, 1982

    5. D-NOMINATE: Dynamic-NOMINATE, 1986-1989