We did a multiple regression to test interaction between A and B on outcome C, using type=complex (MLR) for multilevel data. We got a significant interaction, and plotted and tested whether the slopes at -1SD, mean, and +1SD are different from zero, and found interaction does make sense.
However, we were stuck when describing the magnitude of the interaction effect. I tried 2 ways (model1 and model2 are displayed for later description):
Model 1: C on A B; Model 2: C on A B A*B
1. compute F to test R2 change between model 1 and 2 (this test is given by SPSS when doing hierarchical regression), but result was not significant.
However, because the s.e. was adjusted to be smaller under type=complex, I tried method2:
2. “tricked" Mplus to do Chi-square test for adding A*B (i.e., run Model-1A by fixing the residual variance of C to be same as in Model-2). again, test was not significant.
So, under type=complex,
1)is either above method applicable to test whether A*B explained significant amount of variance? Because, if I get a significant interaction effect, I should get a significant test result for adding A*B, right?
2)is the R2 difference between model1 and model2 the effect size for A*B?
3) What is the correct way of calculating effect size and interpreting magnitude of interaction?
Thanks for your suggestion. I already referred to Aiken & West's book in the past. I guess my question here is essentially whether the interpretation (or method of interpretation) of interaction effect would be any different when using Mplus's "type=complex" feature vs. OLS estimation using other common software such as SPSS or SAS. Can I use the R2, s.e. etc from type=complex analysis to calculate the same statistics that is usually obtained under OLS estimation.