Comparing Stepwise Regression Models to the Best-Subsets Models, or, the Art of Stepwise

Stepwise regression methods are widely recognized as undesirable for explanatory purposes. As exploratory methods, however, they may provide efficient means for researchers to examine multiple models for further investigation. This study used Monte Carlo methods to examine the use of forward and backward regression without stopping criteria (i.e., with customized stepping criteria) in order to create all possible stepwise models (i.e., from one predictor to the fully specified model). Using these stepwise methods without stopping criteria often produced the same models as best-subset regression when there was little multicollinearity. Agreement was still good, but it declined, as multicollinearity became stronger. These results may help us understand the value of stepwise methods for exploratory model building and comparison. These results also suggest the need to examine models using multiple variable selection methods, because when they do not agree, they each may expose different aspects of the complicated theoretical relationships among predictors