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Cluster Correspondence Analysis

Author

Listed:
  • M. Velden

    (Erasmus University Rotterdam)

  • A. Iodice D’Enza

    (Università di Cassino e del Lazio Meridionale)

  • F. Palumbo

    (Università degli Studi di Napoli Federico II)

Abstract

A method is proposed that combines dimension reduction and cluster analysis for categorical data by simultaneously assigning individuals to clusters and optimal scaling values to categories in such a way that a single between variance maximization objective is achieved. In a unified framework, a brief review of alternative methods is provided and we show that the proposed method is equivalent to GROUPALS applied to categorical data. Performance of the methods is appraised by means of a simulation study. The results of the joint dimension reduction and clustering methods are compared with the so-called tandem approach, a sequential analysis of dimension reduction followed by cluster analysis. The tandem approach is conjectured to perform worse when variables are added that are unrelated to the cluster structure. Our simulation study confirms this conjecture. Moreover, the results of the simulation study indicate that the proposed method also consistently outperforms alternative joint dimension reduction and clustering methods.

Suggested Citation

  • M. Velden & A. Iodice D’Enza & F. Palumbo, 2017. "Cluster Correspondence Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 158-185, March.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:1:d:10.1007_s11336-016-9514-0
    DOI: 10.1007/s11336-016-9514-0
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    References listed on IDEAS

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    1. Michel Velden & Tammo Bijmolt, 2006. "Generalized canonical correlation analysis of matrices with missing rows: a simulation study," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 323-331, June.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. Heungsun Hwang & Hec Montréal & William Dillon & Yoshio Takane, 2006. "An Extension of Multiple Correspondence Analysis for Identifying Heterogeneous Subgroups of Respondents," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 161-171, March.
    4. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    5. Vichi, Maurizio & Kiers, Henk A. L., 2001. "Factorial k-means analysis for two-way data," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 49-64, July.
    6. Michel Velden & Yoshio Takane, 2012. "Generalized canonical correlation analysis with missing values," Computational Statistics, Springer, vol. 27(3), pages 551-571, September.
    7. Alfonso Iodice D’Enza & Francesco Palumbo, 2013. "Iterative factor clustering of binary data," Computational Statistics, Springer, vol. 28(2), pages 789-807, April.
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