Linear Regression Analysis: Testing and Elimination of Interaction Terms in Regression and ANOVA

In a regression model, should you remove the interaction terms if they are not significant? In an ANOVA, adding interaction terms still leaves the main effects as main effects. That is, as long as the data is balanced, the main effects and interactions are independent. The main effect still tells you if there is an overall effect for that variable, after considering other variables in the model.

But in regression, adding interaction terms makes the coefficients of the lower-order terms conditional effects, not main effects. That means that the effect of one predictor is conditional on the value of the other. The coefficient of the lower-order term is not the effect of that term. It is the effect only when the other term in the interaction is equal to 0.

So if an interaction is not meaningful, should you leave it?

If you’re just checking for the presence of an interaction to make sure you’re specifying the model correctly, go ahead and drop it. The interaction exhausts gl and changes the meaning of the lower order coefficients and complicates the model. So if you were just looking for it, let it go.

But if you really did hypothesize an interaction that was not significant, leave it in the model. The negligible interaction means something in this case: it helps you test your hypothesis. Taking it out can cause more damage in specification error than in loss of gl.

The same is true for ANOVA models.

And as always, leave in any lower-order terms, significant or not, for any higher-order terms in the model. That means you have to leave all insignificant two-way interactions for any meaningful triples.

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