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VIPSCAL: A combined vector ideal point model for preference data

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  • van Deun, K.
  • Groenen, P.J.F.
  • Delbeke, L.

Abstract

In this paper, we propose a new model that combines the vector model and the ideal point model of unfolding. An algorithm is developed, called VIPSCAL, that minimizes the combined loss both for ordinal and interval transformations. As such, mixed representations including both vectors and ideal points can be obtained but the algorithm also allows for the unmixed cases, giving either a complete ideal pointanalysis or a complete vector analysis. On the basis of previous research, the mixed representations were expected to be nondegenerate. However, degenerate solutions still occurred as the common belief that distant ideal points can be represented by vectors does not hold true. The occurrence of these distant ideal points was solved by adding certain length and orthogonality restrictions on the configuration. The restrictions can be used both for the mixed and unmixed cases in several ways such that a number of different models can be fitted by VIPSCAL.

Suggested Citation

  • van Deun, K. & Groenen, P.J.F. & Delbeke, L., 2005. "VIPSCAL: A combined vector ideal point model for preference data," Econometric Institute Research Papers EI 2005-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1904
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    References listed on IDEAS

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    1. Clyde Coombs, 1975. "A note on the relation between the vector model and the unfolding model for preferences," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 115-116, March.
    2. Forrest Young & Yoshio Takane & Jan Leeuw, 1978. "The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 43(2), pages 279-281, June.
    3. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
    4. Patrick Groenen & Bart-Jan Os & Jacqueline Meulman, 2000. "Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 511-524, December.
    5. Wayne DeSarbo & J. Douglas Carroll, 1985. "Three-way metric unfolding via alternating weighted least squares," Psychometrika, Springer;The Psychometric Society, vol. 50(3), pages 275-300, September.
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    Cited by:

    1. Frank Busing & Mark Rooij, 2009. "Unfolding Incomplete Data: Guidelines for Unfolding Row-Conditional Rank Order Data with Random Missings," Journal of Classification, Springer;The Classification Society, vol. 26(3), pages 329-360, December.

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