Clustering rows and/or columns of a two-way contingency table and a related distribution theory
AbstractThe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 53 (2009)
Issue (Month): 12 (October)
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Louis Guttman, 1971. "Measurement as structural theory," Psychometrika, Springer, vol. 36(4), pages 329-347, December.
- Michael Greenacre, 1988. "Clustering the rows and columns of a contingency table," Journal of Classification, Springer, vol. 5(1), pages 39-51, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.