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Multinomial Restricted Unfolding

Author

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  • Mark de Rooij

    (Leiden University)

  • Frank Busing

    (Leiden University)

Abstract

For supervised classification we propose to use restricted multidimensional unfolding in a multinomial logistic framework. Where previous research proposed similar models based on squared distances, we propose to use usual (i.e., not squared) Euclidean distances. This change in functional form results in several interpretational advantages of the resulting biplot, a graphical representation of the classification model. First, the conditional probability of any class peaks at the location of the class in the Euclidean space. Second, the interpretation of the biplot is in terms of distances towards the class points, whereas in the squared distance model the interpretation is in terms of the distance towards the decision boundary. Third, the distance between two class points represents an upper bound for the estimated log-odds of choosing one of these classes over the other. For our multinomial restricted unfolding, we develop and test a Majorization Minimization algorithm that monotonically decreases the negative log-likelihood. With two empirical applications we point out the advantages of the distance model and show how to apply multinomial restricted unfolding in practice, including model selection.

Suggested Citation

  • Mark de Rooij & Frank Busing, 2024. "Multinomial Restricted Unfolding," Journal of Classification, Springer;The Classification Society, vol. 41(1), pages 190-213, March.
    • Handle: RePEc:spr:jclass:v:41:y:2024:i:1:d:10.1007_s00357-024-09465-3
    DOI: 10.1007/s00357-024-09465-3
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    References listed on IDEAS

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    1. E. Lesaffre & A. Albert, 1989. "Multiple‐Group Logistic Regression Diagnostics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(3), pages 425-440, November.
    2. Yoshio Takane, 1987. "Analysis of contingency tables by ideal point discriminant analysis," Psychometrika, Springer;The Psychometric Society, vol. 52(4), pages 493-513, December.
    3. Willem Heiser, 1991. "A generalized majorization method for least souares multidimensional scaling of pseudodistances that may be negative," Psychometrika, Springer;The Psychometric Society, vol. 56(1), pages 7-27, March.
    4. Dankmar Böhning & Bruce Lindsay, 1988. "Monotonicity of quadratic-approximation algorithms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 641-663, December.
    5. Mark Rooij, 2009. "Ideal Point Discriminant Analysis Revisited with a Special Emphasis on Visualization," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 317-330, June.
    6. de Leeuw, Jan, 2006. "Principal component analysis of binary data by iterated singular value decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 21-39, January.
    7. Louis Guttman, 1968. "A general nonmetric technique for finding the smallest coordinate space for a configuration of points," Psychometrika, Springer;The Psychometric Society, vol. 33(4), pages 469-506, December.
    8. Yoshio Takane & Hamparsum Bozdogan & Tadashi Shibayama, 1987. "Ideal point discriminant analysis," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 371-392, September.
    9. Jan Leeuw, 1988. "Convergence of the majorization method for multidimensional scaling," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 163-180, September.
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