Hello,

I have a question regarding the interpretation of a three-way interaction in a GEE model with a continuous outcome. I am doing this with multiply imputed data. The interaction is between a dichotomous group indicator (x1) and two continuous predictors (x2 and x3). Something like this:

Code:
mi est: xtgee y i.x1##c.x2##c.x3, corr(exch)
The coefficient of the three-way interaction is not significant in the output. However, my particular research question is whether the effect of x2 is significant at higher levels of x3, and whether this interaction differs between the two groups I am considering (signified by the x1 group indicator). So I used margins (or actually, Daniel Klein's great mimrgns command) to obtain the marginal effects of x2 on y at meaningful values of x3, and tested whether those effects differed between the two groups (x1). Something like:

Code:
mimrgns, dydx(x2) at(x1=(0 1) x3=0)) pwcompare
mimrgns, dydx(x2) at(x1=(0 1) x3=1)) pwcompare
mimrgns, dydx(x2) at(x1=(0 1) x3=2)) pwcompare
mimrgns, dydx(x2) at(x1=(0 1) x3=3)) pwcompare
My question is how to interpret these results: there are significant group differences in the effect of x2 at higher levels of x3 (determined with mimrgns and dydx), but the overall three-way interaction is not significant in the regression output. Does this mean that the three-way interaction is significant only at a certain part of the range of x3 and not over the whole range? Or should I not be reporting the significant marginal effects because the overall three-way interaction is not significant.

Thanks for your help,
Robbie