Comparison of Stopping Rules in Forward “Stepwise” Regression

Abstract This paper uses the unconditional mean square error of prediction as a criterion for comparing stopping rules used with the forward “stepwise” selection procedure in multivariate normal samples, based on simulations of 48 population correlation matrices. The CP statistic, “F to enter” (.15 < α < .25), a rule which minimizes the sample criterion, and one which sequentially tests the equality of the population criterion (.25 < α < .35) are superior. For these rules, the criterion seldom differs by more than three percent, although there are considerable differences between these and some of the other rules.