When performing moderation analysis, testing the moderation effect (W) of a given moderator (M, e.g., sex) on the association of a independent variable (X, e.g., age) with a dependent variable (Y, e.g., height):
==> Must X have a statistically significant simple (main) effect on Y on step 1, so that a statistically significant effect of the interation term (W=X*M) is interpreted?
Is this a condition for a mdoeration analysis?
Note: Model 1, A. Hayes' PROCESS.
e.g.:
- Imagine that we are studying if age (X) predicts height (Y);
- And that indeed, age predicts height just in men, but not in women (which stands for a moderation effect of sex on the association between the X and the Y);
- The simple/main effect of age on height in step 1 (which considers the entire sample, men + women) might not be statistically significant because the non statistically significant observed on women may cancel/surpress/blur, the significant effect observed on men, and the interaction/moderation effect on step 3 is statistically significant.
There is absolutely no need for any of the main effects to be significantly different from zero for there to be a significant and meaningful interaction effect. In a so-called disordinal interaction, the main effects may both be zero. For example, a certain type of therapy (medication) may be beneficial for young people but detrimental for old people. You therefore may not see an effect of either therapy (medication vs. placebo) or age (young vs. old) when looking only at the main effects. But the interaction would be very important to look at in that case to understand the differential effect of the medication depending on age. Significant main effects are thus not a prerequisite to test or interpret a moderation (interaction) effect.
Thank you Christian Geiser . As I thought... I have been looking for a reference that supports this thought, but couldn't find it.
There is a very brief mention to this in Baron & Kenny [1986; "There may also be significant main effects for the predictor and the moderator (Paths a and b), but these are not directly relevant conceptually to testing the moderator hypothesis"].
But I haven't found any mention to this elsewhere, despite my best efforst in reading a number of manuals and articles about moderation.
Could you, please, reccomend a reference supporting this, other than Baron & Kenny (1986).
Also, David A. Kenny, in a webinar about the assumptions for moderation analysis talks about the need for causality of Y by X and W, as the 1st assumption [see https://davidakenny.net/webinars/Moderation/Assumptions/Assumptions.html]. So, that's why it was a bit confusing to me, and I would like to have another reference to support this.
In my opinion, there is no need to "support" this with a reference as it is obvious and simply a matter of logic. In fact, with a disordinal interaction, the main effects can be completely misleading/uninterpretable so that you may have to focus only on the interpretation of the interaction effect. In other words, the interaction may be the only relevant effect. (This is one reason why it is always a good idea to plot interaction effects.)
Perhaps you find something when you search for the term "disordinal interaction" together with "main effects." But again, I don't think it is necessary because there is nothing in statistical theory or logic that says you have to show significant main effects before being able to test or interpret and interaction. That would be entirely nonsensical.
Alexandra Ferreira-Valente please see this discussion with an example about the same topic, where we came to the same conclusion as Christian.
https://www.researchgate.net/post/Does_it_make_sense_to_conduct_a_moderation_analysis_if_X_and_Y_are_not_significantly_correlated
In relation to:
"Also, David A. Kenny, in a webinar about the assumptions for moderation analysis talks about the need for causality of Y by X and W, as the 1st assumption [see https://davidakenny.net/webinars/Moderation/Assumptions/Assumptions.html]. So, that's why it was a bit confusing to me, and I would like to have another reference to support this."
This is really a matter of definitions. In statistical terms a moderator effect is merely an interaction between two continuous predictors. So if you interpret moderator effects as being just another term for interaction effects then there is no implied causality.
However, you can have a stricter interpretation in which one variable the moderator (M) causes the change in effect of the other predictor (X).
So this (in my view) amounts to just an issue of what definition you operate under and (trivially) if you want to claim that M has a causal effect on M -> Y you need some reason to justify that.
I think this discussion is confusing moderation (which does not require or expect a relationship between the predictor and the outcome) and mediation (which does require or expect such a relationship). In moderation, the effects tested by the coefficients of the component terms (i.e., X and Z when their product XZ is also in the model) are NOT "main effects." Instead they are the simple effects when the other component equals 0. Consider the model Y = b0 + b1 X + b2 Z + b3 XZ. Factor this to Y = (b0 + b2 Z) + (b1 + b3 Z)X. This shows that the slope relating X to Y depends on the value of Z. When and only when Z = 0 is that slope equal to b1. Hence, transformations such as adding/subtracting a constant from X and Z (as in mean-centering) changes the meaning and value of b1 (but not b3). More details in these articles:
Article Multicollinearity is a red herring in the search for moderat...
Article Misleading Heuristics for Moderated Multiple Regression Models
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