Methodology review: Estimation of population validity and cross-validity, and the use of equal weights in prediction

In multiple regression, optimal linear weights are obtained using an ordinary least squares (OLS) procedure. However, these linear weighted combinations of predictors may not optimally predict the same criterion in the population from which the sample was drawn (population validity) or other samples drawn from the same population (population cross-validity). To achieve more accurate estimates of population validity and population cross-validity, some researchers and practitioners use formulas or traditional empirical methods to obtain the estimates. Others have suggested using the equal weights procedure as an alternative to the formula-based and empirical procedures. This review found that formula-based procedures can be used in place of empirical validation for estimating population validity or in place of empirical cross-validation for estimating population cross-validity. The equal weights procedure is a viable alternative when the observed multiple correlation is low to moderate and the variability among predictor-criterion correlations is low. Despite these findings, it is difficult to recommend one formula-based estimate over another because no single study has included all of the currently available formulas. Suggestions are offered for future research and application of these techniques.