How to interpret an interaction effect in logistic regression models?
I am running a binary logistic regression;
log (Y) = b0 + b1 X1 + b2 x2 + b3 X3 + b4 X2*X3
Y = 1/0
IVs are continuous (X1, X2, X3).
The question is how to plot and interprets the interaction effect (X2*X3)?
Because a moderator(in this case X2) is a variable that can't be measured, What does the interaction of X2 with X3 mean? I'm not sure there is such a thing?
https://www.google.com/search?q=interaction+of+a+moderator+with+a+factor&ie=utf-8&oe=utf-8&client=firefox-b-1
The above link seems to say that moderation and interaction are the same thing. See The first few cites in the link.
Best, David BTW your model is incorrect on the LHS. This makes your question really unclear.
Dear David,
Thank you for your answer.
I know that these two terms (interaction and moderation) are used pretty much interchangeably.
My question is with the presence of an interaction variable (X2*X3) in my model, how we can interpret the effect of X3 on Y at different values of X2 based on the attached figure?
Best, Rebean
You can't, because the interaction X2:X3 tells you that the effect of X2 depends on the value of X3 (and vice versa). The attached figure shows everything. Just interpret that figure:
i) low X2 predicts a high probability of Y, independent of X3
ii) for high X2, the probability of Y depends on X3; it is low for low X3 and increases with increasing X3.
Dear Dr. Rebean
Hello
Dear I think if go through the below link you will get better understating
https://www.theanalysisfactor.com/interpreting-interactions-in-regression/
Regards
@Assas Ali Karam: I don not think that the provided website is very useful as the interpretation of interaction terms in case of probit/logit models is not that straight forward as in linear multiple regression, please se Ai & Norton (2003).
@ Rebean Al-silefanee: Ai & Norton (2003) also suggest how to interpret the results in case of logit/probit models.
Best regards,
Florian
C. Ai and E. C. Norton, “Interaction terms in logit and probit models,” Economics letters, vol. 80, no. 1, pp. 123–129, 2003.
Dear Rebean,
the interpretation of the interaction is quite simple when one of the two variables is a dummy: in that case by interacting them you explore the impact that the IV has on the DV only in the cases when the event attached to the dummy happens. In your case the interpretation is quite difficult. I would say that first and foremost you have to ask yourself the "meaning" of the interacted variable: what are you measuring with it? Secondly, you have to be very careful with the interaction term. Broadly speaking, by multiply one variable for the other, what you obtain is an "aplified" effect of X1 because of X2 (that can be also interpreted of X2 because of X1). Does this amplification make any sense?
My point is that the interpretation is not simply "econometrical": it is mainly "logical" in the sense that it depends on the type of variable and what you are trying to measure with the interaction.
Hope this helps.
Best regards
Andrea
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