Fit DSD - stage 1 vs combined std error calculation

Question

In the screenshot below, the stage 1 analysis shows ~1.4 Std Error for main effects in stage 1.

The combined model shows ~2.4 Std Error for the main effects.

Make Model with only main effects results in ~2.8 SE.

Why does Stage 1 have lower Std Error for main effects than regression with only main effects?

In this example, I set the Stage 2 Ratio to high (5) to eliminate most 2nd order effects.

Thanks in advance for any explanations.

SCS · Answer

Thank-you for replying Mark.

After re-reading the fitting process description I may have a clue. The first stage does not pool inactive factors, the second stage does. Is this correct?

Attached find another simpler example comparing Fit DSD to Make model with a questionable X7 main effect.

The reply box didn't allow pasting images.

DSD fit Example.pptx

Mark_Bailey · Answer

I assume that you have already read the documentation about the Fit Definitive Screening procedure. The example provided displays the same differences in the standard error of the estimates as your example.

The sequential nature of the identification or selection process (i.e., stage 1 and 2) and the presence of 'fake factors' is different from methods based on the regression of the full model. That model is super-saturated leading to a model matrix that is singular.