On the Use of K-Fold Cross-Validation to Choose Cutoff Values and Assess the Performance of Predictive Models in Stepwise Regression

Abstract

This paper addresses a methodological technique of leave-many-out cross-validation for choosing cutoff values in stepwise regression methods for simplifying the final regression model. A practical approach to choose cutoff values through cross-validation is to compute the minimum Predicted Residual Sum of Squares (PRESS). A leave-one-out cross-validation may overestimate the predictive model capabilities, for example see Shao (1993) and So et al (2000). Shao proves with asymptotic results and simulation that the model with the minimum value for the leave-oneout cross validation estimate of predictor errors is often over specified. That is, too many insignificant variables are contained in set βi of the regression model. He recommended using a method that leaves out a subset of observations, called K-fold cross-validation. Leave-many-out procedures can be more adequate in order to obtain significant and optimal results. We describe various investigations for the assessment of performance of predictive regression models, including different values of K in K-fold cross-validation and selecting the best possible cutoffvalues for automated model selection methods. We propose a resampling procedure by introducing alternative estimates of boosted cross-validated PRESS values for deciding the number of observations (l) to be omitted and number of folds/subsets (K) subsequently in K-fold cross-validation. Salahuddin and Hawkes (1991) used leave-one-out cross-validation to select equal cutoff values in stepwise regression which minimizes PRESS. We concentrate on applying K-fold cross-validation to choose unequal cutoff values that is F-to-enter and F-to-remove values which are then used for determining predictor variables in a regression model from the full data set. Our computer program for K-fold cross-validation can be efficiently used for choosing both equal and unequal cutoff values for automated model selection methods. Some previously analyzed data and Monte Carlo simulation are used to evaluate the proposed method against alternatives through a design experiment approach.