Hello,
Sorry this might be a bit of a basic question. For my research, I have three hypotheses. 1)., that NC predicts CA, 2)., that SPS predicts CA, and 3)., that SPS will moderate the relationship between NC and CA.
Originally, I was planning on using a regression to answer hypotheses 1-2, and a moderation analysis for hypothesis 3. However, I am now wondering at whether I can use the main effects in the moderation analysis to answer hypotheses 1-2.
Thank you,
Ross Tumulty.
Yes you can - sort of. First SPS and NC need to be centred (or effect coded if categorical). In the centred model the main effects of SPS and NC will be similar to that in the main effects only model. If there is an interaction however the main effect of NC no longer has the same interpretation as that in the main effects only model. It is the effect of NC when SPS is at its mean (and the interaction implies that the effect of NC varies with SPS). So it becomes the average or typical effect of NC on CA rather than its main effect.
(If there is no interaction the effect of NC dies not depend on SPS and its estimate is the same for any value it takes).
I would like to add to Thom Baguley already good answer:
If there is a non-zero interaction effect, there are no longer main effects, but conditional effects. The effect of NC on CA is dependent on the value which SPS has (in case of centering/effect coding the mean value of SPS). You can see that, if you rearrange the regression equation:
CA ~ b1*NC + b2*SPS + b3*NC*SPS
to
CA ~ (b1 + b3*SPS)*NC + b2*SPS
As you can see, now, the effect of NC on CA is dependent on b1, b3 AND SPS. Only if b3 is == 0, the effect solely depends on b1, which then could be interpreted as a main effect. If b3 0 you have to be careful. In that case it is reasonable to plot the results for different values of SPS to understand how SPS affects the relationship.
Since an interaction is symmetrical, this is also true if you would consider NC as the moderator, of course.
So, if I understand correctly, if the interaction is significant, I could use simple slopes analysis to explore the relationship between NC and CA in the context of the moderation, and the Johnson-Newman technique to explore regions of significance here?
Thank you very much for your guidance and expertise.
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