What does maintaining marginality mean in stepwise regression?

Question

I was reading the helpfile for the dropterm function in the R MASS package, which is one of the main building blocks of the stepAIC function (at least for backwards stepwise regression.) The aim of this function is to identify a variable to remove from a model by sequentially considering models that drop one variable.

In the helpfile, it states:

Try fitting all models that differ from the current model by dropping a single term, maintaining marginality.

What does maintaining marginality mean in this context? Is it a special treatment of interactions specified in the model formula, e.g. by dropping interactions first before dropping the interacting variables?

I suspect it's the principle of marginality. – COOLSerdash Apr 26 '23 at 20:18 — COOLSerdash, Apr 26 '23 at 20:18

Bryan · Accepted Answer · 2023-05-01T12:57:12.647

7

It means that, if you have an interaction, all the lower terms in that interaction are also included in the model. If your model includes "foo:bar", then your model will also include "foo" and "bar" as independent effects.

As mentioned below in comments, this means that any interaction would be dropped before any of its components is dropped.

edited May 01 '23 at 12:57

answered Apr 26 '23 at 20:25

Bryan

1,202

Does this mean foo:bar is dropped first before considering foo and bar to be dropped? – Alex Apr 26 '23 at 20:37
Yes. Yes. Yes. Y – Bryan Apr 27 '23 at 16:22
I will accept your answer if a combination of my comment and your comment is incorporated into it. – Alex May 01 '23 at 03:46

What does maintaining marginality mean in stepwise regression?

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