I'm now testing my hypotheses using a fixed effects model for panel-data (NBA). It's strongly balanced data. Because my hypotheses include two-way interaction and three-way interaction effects, I test my hypotheses using hierarchical regression model.

I include control and independent variables in model 1. let's say each indep var is A, B, & C.

I include two-way interaction variables in model 2 like AB, BC, and A*C

and finally I include three-way interaction variables in model 3, ABC.

My hypotheses are as follows:

  • H1 : A is negatively related to a dependent variable

  • H2 : The relationship in H1 is moderated by B

  • H3 : The moderation in H2 is moderated by C.

The result of the model is as follows:

  • Model 1 (only IV) : A and B is significant while C is insignificant.

  • Model 2 (two-way) : A and B is significant but AB is insignificant.(neither C nor BC nor CA)

  • Model 3 (three-way) : A and B is significant, AB is insignificant but ABC is significant. (other two-way interaction terms and C are also insignificant)

  • I plotted the result and a three-way graph is exactly same as I expected although I didn't conduct slope analysis.

In this case, can I say there is a three-way interaction effect among A,B,C?

I wonder because there is a significant three-interaction term in model 3, but two-way interaction terms are all insignificant in model 2.

I find many postings regarding interaction terms but couldn't find postings regarding both hierarchical regression model and interactions terms.

  • $\begingroup$ Yes, you can say there is a three-way interaction effect. Given this, you should be very cautious in interpreting any of the main effects and two-way effects in any of models 1, 2, or 3. $\endgroup$ – Jacob Socolar Jun 14 '17 at 15:15

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