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Combinatorial Data Analysis: Association and Partial Association

Published online by Cambridge University Press:  01 January 2025

Lawrence J. Hubert
Lawrence J. Hubert*
Affiliation:
The University of California, Santa Barbara
*
Requests for reprints should be sent to Lawrence J. Hubert, Graduate School of Education, The University of California, Santa Barbara, CA 93106.
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Abstract

A combinatorial data analysis strategy is reviewed that is designed to compare two arbitrary measures of proximity defined between the objects from some set. Based on a particular cross-product definition of correspondence between these two numerically specified notions of proximity (typically represented in the form of matrices), extensions are then pursued to indices of partial association that relate the observed pattern of correspondence between the first two proximity measures to a third. The attendant issues of index normalization and significance testing are discussed; the latter is approached through a simple randomization model implemented either through a Monte Carlo procedure or distributional approximations based on the first three moments. Applications of the original comparison strategy and its extensions to partial association may be developed for a variety of methodological and substantive tasks. Besides rank correlation, we emphasize the topics of spatial autocorrelation for one variable and spatial association between two and mention the connection to the usual randomization approach for one-way analysis-of-variance.

Keywords

partial associationpartial correlationnonparametric statisticsspatial statisticspermutation tests
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 4 , December 1985 , pp. 449 - 467
Copyright
Copyright © 1985 The Psychometric Society

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