# Is it proper to specify the interaction term between two independent continuous variables of model A) as the dependent variable in a second model B)?

1. Main problem

I am struggling with a mediation – moderation question. Is it proper to specify the interaction term between two independent continuous variables of model A) as the dependent variable in a second model B)? If yes, what does the final specification look like?

Model A): Y = a0 + a1x1 + a2x2 + a3x3 + a4(x1*x3) + error_A

Model B): x1*x3 = b0 + b1x2 + error_B

2. Aim of the model

I would like to answer the question, how the variable x2 influences the moderation process (interaction term) in model A.

Specifying it as a three-way interaction instead (Y = a0 + a1x1 + a2x2 + a3x3 + a4(x1*x3) + a5(x1*x2) + a6(x2*x3) + a7(x1*x2*x3) + error) doesn't seem right, because there is a strong relationship between x2 and at least one of the variables, which are part of the interaction term (x1 and x3).

I read through the material provided by Andrew Hayes, but apparently non of the templates (he offers wonderful templates as part of his PROCESS macro for SPSS to do moderation analyses) suites my needs.

I guess what I conceptually need, is the mediation model which results when I combine Model A) and B):

Model C): Y = a0 + a1x1 + a2x2 + a3x3 + a4(b0 + b1x2 + error_B) + error_A

Moreover, since I expect x2 to influence the interplay of x1 and x3, I guess I need to incorporate the influences of x2 on x1 and x3 as well.

Model D): x1 = d0 + d1x2 + error_D

Model E): x3 = e0 + e1x2 + error_E

Model F): Y = a0 + a1(d0 + d1x2 + error_D) + a2x2 + a3(e0 + e1x2 + error_E) + a4(b0 + b1x2 + error_B) + error_A

4. How I would go about it

Basically, all I would technically do is specify four regression models (Model A, Model B, Model D and Model E) and then summarize the coefficients, such that the change in Y as a result of a one step increase in x2 can be expressed as: a1*d1*x2 + a2*x2 + a3*e1*x2 + a4*b1*x2.