Goodman and Kruskal's lambda: a new look at an old measure of association.

Abstract:

:We examine Goodman and Kruskal's lambda using Efron's approach to regression and analysis of variance (ANOVA) for zero-one outcome data. For a binary response cross-classified by a single nominal predictor, we present a computationally simple ANOVA table in which lambda is analogous to Pearson's R-square. We characterize the relationship between lambda and the commonly used apparent error rate in logistic regression, and show that lambda is based implicitly on a prediction rule for a saturated model with classification level 0.5. This relationship suggests that we can correct the apparent error rate for chance by defining a natural generalization of lambda that we call PRE, the proportional reduction in error. We illustrate the use of lambda and PRE in an analysis of prognostic factors for one-year survival in children with the acquired immunodeficiency syndrome (AIDS).

journal_name

Stat Med

journal_title

Statistics in medicine

authors

Makuch RW,Rosenberg PS,Scott G

doi

10.1002/sim.4780080511

subject

Has Abstract

pub_date

1989-05-01 00:00:00

pages

619-31

issue

5

eissn

0277-6715

issn

1097-0258

journal_volume

8

pub_type

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