Estimators for Two Measures of Association for Set Correlation

Abstract

Two measures of association between sets of variables X and Y have been proposed for set correlation, RY,X2 as a proportion of generalized variance and TY,X2 as a proportion of additive variance. Because these measures are strongly positively biased, approximate expected values and estimators of these measures are derived and checked by means of a Monte Carlo study. It is noted that sample values are subject to more "shrinkage" than is the multiple R2, and that, therefore, it is desirable to determine routinely the estimators' values. It is recommended that as a rule of thumb, the ratio of sample size to the product of the numbers of variables in the two sets should be at least 20, and preferably 25 or 30.