0
$\begingroup$

This seems like a simple question, but I can't seem to find a clear answer, so perhaps it isn't...

Let's suppose I fit a two-way linear model with interaction term. So in R,

fullmodel <- lm(Y ~ A * B)

now

summary(model)

will give me marginal significance values for A, B and the A*B interaction. Looking at my output, I note that the interaction is significant, meaning that given that A and B are in the model, adding the interaction between them is warranted.

But I want to test the hypothesis that "B is important in predicting Y". To do this, my instinct is to use ANOVA to compare a model with B to one without.

ANOVA(modelwithB, modelwithoutB)

To me, it seems logical that

modelwithoutB <- lm(Y ~ A)

and so the comparison should be

ANOVA(fullmodel, modelwithoutB)

This means that I compare a model with just A to one with both a main effect of B and an A*B interaction. Do people concur? Or is there something flawed in my reasoning (or perhaps in my hypothesis)?

$\endgroup$
  • $\begingroup$ this seems correct. $\endgroup$ – Ben Bolker Jan 5 '18 at 0:54
  • $\begingroup$ Welcome to the stats.stackexchange.com. Indicate briefly about sample data and characteristics of data as well as your objectives. $\endgroup$ – Subhash C. Davar Jan 5 '18 at 0:57
0
$\begingroup$

I think you should plot the interaction to try to understand it better. From a statistical/technical standpoint, you are right. The comparison is a to the main effect and intersection. My concern is if you are missing something substantively important by doing this.

$\endgroup$
0
$\begingroup$

Thanks. Of course you are right about examining the interaction, and in this case the comparison I describe does produce significance for B so I would be examining the full model. This question was prompted by a table of marginal significances in which the B main effect is weak and non-significant but the A*B interaction is strong and significant. (And the A main effect is significant.) My interpretation of this is that B acts largely as a modifier of the relationship between Y and A. And I suppose I could demonstrate B being 'important' simply by pointing to the t-test significance of the marginal effect of the interaction. But my understanding is that there could be a case in which both the main effect and the interaction are not significant on their own, but the F test I describe (Y ~ A + B + A:B vs Y ~ A) is.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.