Determination of the best significance level in forward stepwise logistic regression

The χ2 test based on a fixed a level (χ2 (a)) is the standard stopping criterion in forward stepwise logistic regression. SAS/IML programs were written to provide Monte Carlo simulations to determine the best a level for the χ2 (a) stopping criterion. Performance was evaluated using Efron's (1986) estimated true error rate of prediction. The best a varied between 0.05 and 0,40. In all cases, it increased linearly the number of predictor variables; in the multivariate binary case, it also depended upon the mean of the binary variables in one population and the difference between the means of the binary variables in the two populations. An overall recommendation is that 0.15 ≤ a ≤ 0.20 should be used for the χ2 (a) stopping criterion.