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If I have a model that is Y~A+B, where only A is significant (low p-value). After adding an interaction term to form a new model Y~A+B+(AB), B remains not significant but the interaction term (AB) is significant.

I have read that "Note that, an interaction term is added into the model when the main term is already in the model. For example, we should not have the term $x_1x_2$ in the model if there is no term $x_2$ or $x_1$."

Would this be an issue since I am not dropping the not significant term (in this case B)? Do I fit Y~A or Y~A + B + (AB) since I don't think it is appropriate to fit Y~A + AB?

Marwin
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  • Welcome! Not only should you fit the interaction model with the corresponding main effects, but you will often be forced to in practice. In some software packages, including a product term in a model automatically results in the estimation of the main effects. Now, just because you should not omit the main effect does not mean you cannot in practice. The interpretation or A*B will be different if you omit A or B. I think a lot of ground was covered in this post. – Thomas Bilach Apr 05 '20 at 18:32

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You should fit Y ~ A + B + AB.

A model with two main factors should include the interaction term because we need to know how to interpret the main factor results.

If the interaction term is not-significant then the main effects can be interpreted directly (they are constant). Different levels of factor A always have the same effect.

But if the interaction term is significant, then the effect of factor A depends on the level of factor B (the effect of factor A is not constant).

Groovy_Worm
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