Understanding interaction and SmartPLS Outputs

[krismurphy01]

Unfortunately, I feel that I am about to state the obvious but after much work I am just not sure that I understand an interaction effect. Here is the situation.... I have a moderator that I would like to use to test interactions - simple enough. Let's call this variable A. Then I have three independent variables (variables B,C and D) that impact a dependent variable - let's call this variable X. The direct relationships on the dependent variable are as follows.

Direct effects:
A has negative effect on X (note that the path is around .225) - moderator on DV.
B has negative effect on X (small and not significant at .100)
C has positive effect on X (small and but significant at .200)
D has positive effect on X (note that the path is around .314)

The interaction effects using the product approach (I tried all approaches and the results were very similar):
AxB on X has a positive effect
AxC on X has a negative effect

drum roll....
AxD on X has a positive effect (the path is about .180 and is significant)

My questions are:
1. Does the positive effect of AxD on X make sense?
2. How does one interpret the slope charts with the scale running from 1 to -1. (Does the SD mean stand deviation?) (how is the 1 and -1 derived)
3. Is it possible to create a high / low chart using the slope chart or data? If so, how?

Here is my attempt to figure out what is happening:
1. All three interaction relationships are correct.
2. The effect of variable D is stronger than the negative effects of variable A. I think the that the high / low and SD slope chart matter here.

Why did I post these questions? Because I was expecting the effect of AxD on X to be negative. I'm hoping for that someone can help me with an intelligent response that might be..Kris, it is not about simply multiplying the negative effects against the positive effects of variable D but more about the total effect on variable X which you note as being less than the direct relationship of D on X.

I am not sure how I may create a high / low chart using an interaction type approach. My main issue is that the line does not intercept because I think it is moving within the distribution in terms of deviations. Is it even possible to test for high / low effects using an interaction term?

Thanks in advance for any help you can provide. Note that I could not find the answers in the Hair et al. book which very useful and a great read.

[jmbecker]

The interpretation of an interaction is
How does the effect of B, C, and D on X change with the level of A?
If you have an negative interaction effect (AxC), the effect of C on X reduces with higher A. Because you have a positive effect of C and X the positive effect is getting smaller with larger A. It may even get negative if A is large enough. On the contrary, if A is small, your effect of C on X is larger. The direct effect of C on X is actually the effect at the mean of A, because we standardize and standardization implies mean centering.

It is always good to rewrite your equations to illustrate interaction effects.
X = a +beta1A + beta2 B + beta3 AxB
<=> X = a + beta1 A + (beta2 + beta3 A)B

If A is 0 (in case of mean centering or standardization at the mean of A) then B has only its direct impact beta2. If A is larger than 0 (the mean) you add beta3 and if A is smaller than 0 (the mean) you subtract beta3. If beta 3 is negative then the direction changes of course.

Hence, you have to think about your hypothesis for the moderator and if it should reduce or enhance effects, if it is getting larger/smaller.