title: An asymptotic partial correlation test for the Goodman-Kruskal lambda.
abstract: Goodman and Kruskal introduced a measure of predictive association when predicting the category of a variable A from a category of a variable B. This measure, denoted lambda, is the asymmetric proportional reduction in error measure in predicting an individual's A category that can be eliminated by using knowledge of the B classification. It takes values on the unit interval, with a zero value meaning no predictive gain, while a value of unity indicates a perfect predictive association between A and B. A test of H(0): lambda = 0 versus H(1): lambda > 0 is analogous to a test for the significance of the correlation coefficient. A test of the partial lambda coefficient, which is analogous to a test of the partial correlation coefficient, answers the question of whether knowledge of an additional third (or higher) classification or categorical variable results in a significant increase in predicting the variable A. Suich and Turek developed an exact test for the partial lambda coefficient, but only for the situation where the predicted categorical variable A is dichotomous. The present paper completes the previous work by developing an asymptotic test where the predicted category A is any polytomous variable.
authors.affiliation: Department of Information Systems/Decision Sciences, California State University, Fullerton, CA 92834, USA. rsuich@fullerton.edu
authors.forename: Ronald C
authors.initials: RC
authors.lastname: Suich
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Turek
mesh_terms: D006801:Humans; D008960:Models, Psychological; D011237:Predictive Value of Tests; D011581:Psychological Tests / Q000706:statistics & numerical data*