Using Wherry's Adjusted <i>R</i> ² and Mallow's <i> C _p </i> for Model Selection From All Possible Regressions

Abstract

Abstract Selecting a subset of predictors from a pool of potential predictors continues to be a common problem encountered by applied researchers in education. Because of several limitations associated with stepwise variable selection procedures, the examination of all possible regression solutions has been recommended. The authors evaluated the use of Mallow's Cp and Wherry's adjusted R 2 statistics to select a final model from a pool of model solutions. Neither the Cp nor the adjusted R 2 statistic correctly identified the underlying regression model any better and was generally worse than the stepwise selection method, which itself was poor. Using any of the model selection procedures studied here resulted in biased estimates of the authentic regression coefficients and underestimation of their standard errors. The use of theory and professional judgment is recommended for the selection of variables in a prediction equation.