PROC GLMSELECT with SELECTION=STEPWISE is run. A variable is added at step 3, removed at step 5, and added again at step 8. What does this cycling indicate?
Select an answer to reveal the explanation.
Short Explanation
Here's the deal — when a variable enters, leaves, and re-enters during stepwise selection, you're seeing instability from correlated predictors. A correlated variable can absorb variance that made the cycling variable look useful, so it drops out, then comes back when that correlated variable leaves.
Full Explanation
The correct explanation is that multicollinearity among correlated predictors causes instability in the stepwise selection path; the variable's partial contribution changes as other correlated variables enter or leave. When a correlated variable enters the model, it absorbs variance that the cycling variable explained, causing it to be removed. When that correlated variable is later removed, the cycling variable re-enters. This instability indicates multicollinearity and casts doubt on the reliability of stepwise results. The claim that the variable is a strong predictor and should definitely be included is wrong because cycling indicates instability, not strong evidence of importance. The claim that PROC GLMSELECT has a bug is wrong because cycling is a documented statistical phenomenon, not a software bug. The claim that the cross-validation criterion changed between steps is wrong because the selection criterion is fixed throughout a PROC GLMSELECT run.