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I'm currently sitting on a research project and I got an output which is confusing me.

The hypothesis to be checked is: Self-Efficacy (Centered_KOMP) is moderating the negative relationship between Neuroticism (CENTERED_NEUR) and Meaning in Work (SUM_ME_WORK). I ran a hierarchical multiple regression analysis with only the main effects in the first step and added the interaction effect in a second step.

In the first step, the main effects both were significant. In the second model with the interaction, the main effect of self-efficacy on Meaning in Work became insignificant. The interaction effect was significant though.

A tutor of mine said that this was an unusual result, which made me insecure about interpreting this effect. My questions are:

How can I interpret this?

What's an explanation for this result? Do Standard Deviations & Ranges (Variability) maybe provide an explanation for this? (CENTERED_NEUR has SD = 26.14; and a high range (107) = high variability?) (CENTERED_KOMP has SD = 5.34 with a range of 21 -> lower variability?) The Neuroticism scale incorporated 20 Items with options ranging from 1 - 7, the self-efficacy scale incorporated six items with options ranging from 1-5)

So far, I interpreted like this, but I'm very unsure if that's correct: The interaction effect might be explaining most of the variability the main effect of self-efficacy was previously accounting for. The effect of self-efficacy might only be significant at certain levels of neuroticism (although I'm unsure, since wouldn't this imply that neuroticism is a moderator, too?)

I would much appreciate the help!!!

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When you add an interaction effect, the meaning of the main effects changes. You should not try to interpret the main effects without also considering the interaction effect.

Your equation with main effects only is (something like):

$M = \beta_0 + \beta_1\times K + \beta_2 \times N $

You can usually ignore $\beta_0$ in this situation. You can add or subtract a constant from from K or N, and there will be no effect on $beta_1$ or $\beta_2$.

But now you add the interaction term:

$M = \beta_0 + \beta_1\times K + \beta_2 \times N + \beta_3 \times K \times N $

But think about how to interpret the main effects, when the interaction is there. Let's use a value of 0 for K (because that makes the math easier). So we substitute 0 for K.

$M = \beta_0 + \beta_1\times 0 + \beta_2 \times N + \beta_3 \times 0 \times N $

And then we remove anything that is multiplied by zero.

$M = \beta_0 + \beta_2 \times N $

So the main effect of N is the estimated effect when K is zero.

Make K a different number, and the main effect changes - so if you add or subtract a constant from K, and then run the model, the main effect of N will change. If you do that in a model without interaction, it will have no effect.

So your tutor is (with all respect) wrong. This is not an unusual effect, it is absolutely expected and normal.

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  • $\begingroup$ Thank you for your reply. So since this seems to be not an unusual effect, do I need to look at Standard Deviations (variability of variables) at all to explain the effect? "The interaction effect might be explaining most of the variability the main effect of self-efficacy was previously accounting for. The effect of self-efficacy might only be significant at certain levels of neuroticism" -> and is this a correct interpretation? $\endgroup$
    – MadameLibelle
    Commented Jun 20 at 13:16
  • $\begingroup$ You can tell by looking at the r-sqiared change when you add the interaction effect. $\endgroup$
    – Jeremy Miles
    Commented Jun 20 at 13:45
  • $\begingroup$ The R Squared change is .030. It changes from R^2 .385 in the first step to R^2 .415 in the second step $\endgroup$
    – MadameLibelle
    Commented Jun 20 at 13:50
  • $\begingroup$ That's pretty small. Also, you say "The effect of self-efficacy might only be significant at certain levels of neuroticism" - well yes, of course. That's what an interaction means - at some levels of N, the effect of S is zero, so it is not significant. You could look at the work on regions of significance, e.g. quantpsy.org/interact $\endgroup$
    – Jeremy Miles
    Commented Jun 20 at 18:09

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