Do Not Misstep

R. Mark Sharp

10/4/2018

Open Ridicule By Statisticians

• Stepwise regression is important in developing prediction models only in the sense that it is important to avoid its use.

• Stepwise variable selection has done incredible damage to science. How did we statisticians let this happen?

• A journey of a thousand hypotheses begins with a single stepwise regression

Statistical Issues

• Yields R-squared values that are biased to be high.
• Based on methods (e.g., F tests for nested models) intended to be used to test prespecified hypotheses.
• F and \(\chi^2\) tests do not have the claimed distribution.
• Yields p-values that do not have the proper meaning, and the proper correction for them is a difficult problem.
• Gives biased regression coefficients that need shrinkage

Effects

• Has severe problems in the presence of collinearity.
• Increasing the sample size does not help much. The size of the sample was of little practical importance in determining the number of authentic variables contained in the final model.
• The number of candidate predictor variables affected the number of noise variables that gained entry to the model.
• Method yields confidence intervals for effects and predicted values that are falsely narrow