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I am interested in studying the interaction with a ordinal predictor p and continuous moderator m on an outcome y with a simple model of:

y ~ p + m + p*m

However, since my predictor is categorical, it is easier for me to plot how the relationship between outcome y and moderator m (both continuous) changes for different categories of predictor p.

That is, y is on the y axis, m is on the x axis and I draw several lines with different slopes for each category of predictor p. Would this be a valid way to plot the interaction effect if I am ONLY interested in the moderation effect of m and not its direct relationship with outcome y?

I think it is because if there is an interaction effect, then it should be bidirectional- that is, m modifies the relationship between y and p and p would modify the relationship between y and m, is that correct?

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Just from a methodological view:

if you plot the interaction of P*M on Y and put m on the x-axis, then p becomes your moderator as you are plotting the effect of M on Y, conditional on the level of P.

However, mathematically it does not make a difference. Which brings me to the answer to your question. A interaction is always "bidirectional" as you call it. You multiply M*P and from a mathematical point of view, it makes no difference which you consider the moderator the results would not change.

So you are correct when saying "m modifies the relationship between y and p and p would modify the relationship between y and m".

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  • $\begingroup$ Right that is my concern as well as I am reversing the role of the moderator and predictor, so I am not sure if my graph makes sense at all. For example, if I see a difference in slopes across levels of P, then clearly P modifies M. However, does that also imply that M modifies P to a similar degree? $\endgroup$
    – Hank Lin
    Commented Dec 5, 2018 at 12:50
  • $\begingroup$ Yes, if you did not dummy code your varaible. So in your regression equation Y~b0+b1*p+b2*m+b3*(p*m), the b3 is the interaction effect, this effect is added on top of the b0+b1*p+b2*m. So lets assume P=1 and M=5, then b3(1*5) or differently 5 times the regression coefficient are added. If P=1 and M=6 then 6 time the regression coefficient is added. If P=2 and M=5 then 10 times the interaction effect is added. The interaction effect itself remains the same. But a change in P has a bigger effect on the estimate because the scale of P is smaller than the one of M. $\endgroup$
    – Janosch
    Commented Dec 5, 2018 at 12:58
  • $\begingroup$ Actually, p is dummy coded as it is an ordinal variable, but m is continuous- how does that affect the interpretation? $\endgroup$
    – Hank Lin
    Commented Dec 6, 2018 at 10:32

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