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Nonparametric Unfolding of Binary Choice Data

  • Keith T. Poole (a1)

This paper shows a general nonparametric unfolding technique for maximizing the correct classification of binary choice or two-category data. The motivation for and the primary focus of the unfolding technique are parliamentary roll call voting data. However, the procedures that implement the unfolding also can be applied to the problem of unfolding rank order data as well as analyzing a data set that would normally be the subject of a probit, logit, or linear probability analysis. One aspect of the scaling method greatly improves Manski's “maximum score estimator” technique for estimating limited dependent variable models. To unfold binary choice data two subproblems must be solved. First, given a set of chooser or legislator points, a cutting plane must be found such that it divides the legislators/choosers into two sets that reproduce the actual choices as closely as possible. Second, given a set of cutting planes for the binary choices, a point for each chooser or legislator must be found which reproduces the actual choices as closely as possible. Solutions for these two problems are shown in this paper. Monte Carlo tests of the procedure show it to be highly accurate in the presence of voting error and missing data.

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David Andrich . 1995. “Hyperbolic Cosine Latent Trait Models for Unfolding Direct Responses and Pairwise Preferences.” Applied Psychological Measurement 19: 269290.

Joseph F. Bennett , and William L. Hays 1960. “Multidimensional Unfolding: Determining the Dimensionality of Ranked Preference Data.” Psychometrika 25: 2743.

Alvin M. Best , Forrest W. Young , and Robert G. Hall 1979. “On the Precision of a Euclidean Structure.” Psychometrika 44: 395408.

Ingwer Borg , and Patrick Groenen . 1997. Modern Multidimensional Scaling: Theory and Applications. New York: Springer-Verlag.

Clyde Coombs . 1950. “Psychological Scaling Without a Unit of Measurement.” Psychological Review 57: 148158.

Wayne S. DeSarbo , and Jaewun Cho . 1989. “A Stochastic Multidimensional Scaling Vector Threshold Model for the Spatial Representation of ‘Pick Any/N’ Data.” Psychometrika 54: 105129.

Wayne S. DeSarbo , and Donna L. Hoffman 1987. “Constructing MDS Joint Spaces from Binary Choice Data: A Multidimensional Unfolding Threshold Model for Marketing Research.” Journal of Marketing Research 24: 4054.

Carl Eckart , and Gale Young . 1936. “The Approximation of One Matrix by Another of Lower Rank.” Psychometrika 1: 211218.

James J. Heckman , and James M. Snyder 1997. “Linear Probability Models of the Demand for Attributes With an Empirical Application to Estimating the Preferences of Legislators.” Rand Journal of Economics 28: 142189.

Hiroshi Hojo . 1994. “A New Method for Multidimensional Unfolding.” Behaviormetrika 21: 131147.

James C. Lingoes 1963. “Multiple Scalogram Analysis: A Set-Theoretic Model for Analyzing Dichotomous Items.” Education and Psychological Measurement 23: 501524.

John B. Londregan 2000. “Estimating Legislators’ Preferred Points. Political Analysis 8(1): 3556.

Charles F. Manski 1975. “Maximum Score Estimation of the Stochastic Utility Model of Choice.” Journal of Econometrics 3: 205228.

Charles F. Manski 1985. “Semiparametric Analysis of Discrete Response: Asymptotic Properties of the Maximum Score Estimator.” Journal of Econometrics 27: 313333.

Charles F. Manski , and T. Scott Thompson 1986. “Operational Characteristics of Maximum Score Estimation.” Journal of Econometrics 32: 85108.

John Ross , and Norman Cliff . 1964. “A Generalization of the Interpoint Distance Model.” Psychometrika 29: 167176.

Peter H. Schonemann 1966. “A Generalized Solution of the Orthogonal Procrustes Problem.” Psychometrika 31: 110.

L. Spector , and M. Mazzeo 1980. “Probit Analysis and Economic Education.” Journal of Economic Education 11: 3744.

Wijbrandt H. Van Schuur 1992. “Nonparametric Unidimensional Unfolding for Multicategory Data.” In Political Analysis, Vol. 4, ed. John H. Freeman Ann Arbor: University of Michigan Press.

Gale Young , and A. S. Householder 1938. “Discussion of a Set of Points in Terms of their Mutual Distances.” Psychometrika 3: 1922.

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Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
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