We deal with the problem of evaluating the strength of the dependency of a categorical response variable upon a categorical explanatory variable by means of the Goodman and Kruskal's τ. For given marginals, τ seldom reaches its theoretical upper bound, 1. It seems therefore reasonable to determine the maximum value the index can assume in a class of contingency tables with given marginals. Three kinds of heuristics developed to this aim are presented. An upper bound for the maximum is determined so that it is possible to estimate the relative error of the proposed heuristics.
Sharp bounds for the maximum of the Goodman-Kruskal τ index in a class of I x J tables with given row and column totals
PICCARRETA, RAFFAELLA
1999
Abstract
We deal with the problem of evaluating the strength of the dependency of a categorical response variable upon a categorical explanatory variable by means of the Goodman and Kruskal's τ. For given marginals, τ seldom reaches its theoretical upper bound, 1. It seems therefore reasonable to determine the maximum value the index can assume in a class of contingency tables with given marginals. Three kinds of heuristics developed to this aim are presented. An upper bound for the maximum is determined so that it is possible to estimate the relative error of the proposed heuristics.
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