Quick question about the moderator variable

[Omar Shaher]

Dear Researchers,

If I have assumed that Y is the dependent variable and X is the independent variable, and A is the moderator variable. And, also if the model will be as below:
Y = X + A + X*A
So, is there a statistical condition that requires, before examining the moderate effect, to show that there is a relationship between the moderator and the dependent variable on the one hand, and on the other hand, showing that there is a relationship between the moderator and the independent variable through empirical evidence in the literature?

If no, what if the previous literature has studied the above-mentioned relationships without examining the moderating effect on the relationship between the dependent and independent variable? Shall I mention all the previous relationships?

Many thanks in advance.

[Maarten Buis]

For a mediating effect you need X to influence A and A in turn needs to infuence Y. For a moderating effect that is not necessary. There you assume that X has different effects on Y depending on A.

[Omar Shaher]

Thanks, Maarten, for your answer. Much appreciated.

So, if we are assuming that there is a relationship between X and Y, also there is a relationship between A and Y, and also there is a relationship between A and X, then we should examine the mediator effect, not the moderator BUT if we are assuming that X has different effect on Y depending on A, we should mention all literature that supports the relation between Y and X, and in turn A and Y, without mentioning the literature that support the relationship between X and A, and on that way, we can examine the moderator. Is this what you are trying to say?

Thank you.

[Maarten Buis]

That is largely fine. I would add that you would need to have a reason to believe that the effect of X on Y depends on A. This reason could (some disciplines say should) be your theory (other disciplines allow you to use previous research as a justification).