A Monte Carlo evaluation of three formula estimates of cross-validated multiple correlation.

To determine the stability of regression equations, researchers have typically employed a cross-validation design in which weights are developed on an estimation subset of the sample and then applied to the members of a holdout sample. The present study used a Monte Carlo simulation to ascertain the accuracy with which the shrinkage in R–2 could be estimated by 3 formulas developed for this purpose. Results indicate that R. B. Darlington's (see record 1968-08053-001) and F. M. Lord (1950) and G. E. Nicholson's (1960) formulas yielded mean estimates approximately equal to actual cross-validation values, but with smaller standard errors. Although the Wherry estimate is a good estimate of population multiple correlation, it is an overestimate on population cross-validity. It is advised that the researcher estimate weights on the total sample to maximize the stability of the regression equation and then estimate the shrinkage in R–2 that he/she can expect when going to a new sample with either the Lord-Nicholson or Darlington estimation formulas. (17 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)