Hello everyone! I am currently doing moderation/mediation analyses with Hayes Process.
As you can see the model 3 is significant with R2=.48
The independent variables have no sig. direct effect on the dependent variable, but significant interaction effects. The curious thing is: toptMEAN does not correlate with any of the variables, but still fits into the regression model. Should I take this as confirmation that toptMEAN has an effect on the dependent variable even though it does not correlate? Or am I missing something in the interpretation of these results?
(Maybe you could also suggest a different model for me to run. model 3 is currently the one with the highest r2 i found)
I want to add: I also did a regression with another variable, where it`s basically the other way around and its very confusing - this one correlates with all the others, model is significant but(!) there are no significant interaction effects.
It is very well possible to have significant interaction effects but no significant "main" effects. It is also possible to have significant "main" effects and no significant interactions. And it is possible that variables have significant zero-order correlations with the dependent variable but no significant regression coefficients (e.g., due to redundancies and/or overfitting of the regression model). Finally, it possible to find non-significant zero-order correlations between IVs and DV but significant regression coefficients (e.g., due to suppression effects).
Many of these effects cannot easily be identified from the zero-order correlations. That's one reason why we run multiple regression analyses--to identify redundancies, interactions, suppression effects, etc. that are not easy to see in a bivariate correlation analysis.
Note also that the "main" (lower-order) effects (and their significance) in the moderated regression model depend on whether you centered the predictors or not. This can make a huge difference for the interpretation. Especially when predictor variables do not have a meaningful zero point, centering prior to calculating the interaction terms is recommended (e.g., Aiken & West, 1991; Cohen et al., 2003). Otherwise, the lower-order terms (and their significance) may not be interpretable at all.
In any case, it would be a good idea for you to plot the effects to get a better understanding of what is going on. That is, look at the regression lines for different values of your moderators to understand the meaning of the interaction effects.
Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park: Sage.
Cohen, J., Cohen, P., West, S. G. & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences. Mahwah, NJ: Erlbaum. (Chapters 7 and 9)
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