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Clustering rows and/or columns of a two-way contingency table and a related distribution theory

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  • Hirotsu, C.
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    Abstract

    The row-wise multiple comparison procedure proposed in Hirotsu [Hirotsu, C., 1977. Multiple comparisons and clustering rows in a contingency table. Quality 7, 27-33 (in Japanese); Hirotsu, C., 1983. Defining the pattern of association in two-way contingency tables. Biometrika 70, 579-589] has been verified to be useful for clustering rows and/or columns of a contingency table in several applications. Although the method improved the preceding work there was still a gap between the squared distance between the two clusters of rows and the largest root of a Wishart matrix as a reference statistic for evaluating the significance of the clustering. In this paper we extend the squared distance to a generalized squared distance among any number of rows or clusters of rows and dissolves the loss of power in the process of the clustering procedure. If there is a natural ordering in columns we define an order sensitive squared distance and then the reference distribution becomes that of the largest root of a non-orthogonal Wishart matrix, which is very difficult to handle. We therefore propose a very nice [chi]2-approximation which improves the usual normal approximation in Anderson [Anderson, T.W., 2003. An Introduction to Multivariate Statistical Analysis. 3rd ed. Wiley Intersciences, New York] and also the first [chi]2-approximation introduced in Hirotsu [Hirotsu, C., 1991. An approach to comparing treatments based on repeated measures. Biometrika 75, 583-594]. A two-way table reported by Guttman [Guttman, L., 1971. Measurement as structural theory. Psychometrika 36, 329-347] and analyzed by Greenacre [Greenacre, M.J., 1988. Clustering the rows and columns of a contingency table. Journal of Classification 5, 39-51] is reanalyzed and a very nice interpretation of the data has been obtained.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 53 (2009)
    Issue (Month): 12 (October)
    Pages: 4508-4515

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    Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4508-4515

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    Web page: http://www.elsevier.com/locate/csda

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    1. Michael Greenacre, 1988. "Clustering the rows and columns of a contingency table," Journal of Classification, Springer, vol. 5(1), pages 39-51, March.
    2. Louis Guttman, 1971. "Measurement as structural theory," Psychometrika, Springer, vol. 36(4), pages 329-347, December.
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