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I was given an ANOVA table and asked to reduce the model sequentially.

I searched the online resources say: When reducing the model sequentially, you typically start by assessing the significance of high-order terms and then proceed to lower-order terms if necessary.

Does that mean when reducing a model, we always begin by examining the highest-order interaction terms with the highest p-values, then remove any non-significant terms, and subsequently refit the model?

Thanks!

Matata
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First, it does not yield that. This method would select only mix and plasticizer.

The reason for looking at interactions first is because it is almost always a good idea to include the main effects that are part of an interaction. So, if you keep an interaction, you should keep the main effects that are part of it.

But this whole approach is wrong. It is a form of backwards selection. It doesn't work well. The results will be wrong: The p values too low, the standard errors too small, and the parameter estimates biased away from 0.

See the model selection tag and particularly this thread.

In general, it is not safe to rely on "online resources", unless the author is established. This site is an exception, because answers can be commented on, voted down, flagged, or even removed if they are incorrect. They can also be voted up or accepted if they are useful.

Peter Flom
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    (+1) This answer leads me to believe that there should be a mandatory chapter in every statistics book about this method. It is annoyingly prevalent in my field despite its long-studied problems. – Shawn Hemelstrand Mar 07 '24 at 10:31
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    Answers can be commented, flagged and voted (up or down). – Richard Hardy Mar 07 '24 at 11:04
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    @ShawnHemelstrand sometimes backward selection can be used, with caution. Frank Harrell allows for: "limited backwards step-down variable selection if parsimony is more important that accuracy... But confidence limits, etc., must account for variable selection (e.g., bootstrap)." The adjustment for the variable selection is what's typically omitted in practice. – EdM Mar 07 '24 at 18:01