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Re: st: inteff and mfx?

From   Maarten Buis <>
Subject   Re: st: inteff and mfx?
Date   Thu, 19 Apr 2012 09:57:46 +0200

On Wed, Apr 18, 2012 at 6:57 PM, Luca Fumarco wrote:
> I have a question concerning the marginal effect of an interaction term; the model I am using is the probit.
> -Buis, yyyy, "Simple interpretation of interaction in non-linear models", Tha Stata Journal

Correct reference is:
M.L. Buis (2010) "Stata tip 87: Interpretation of interactions in
non-linear models", The Stata Journal, 10(2), pp. 305-308.

> Now I am trying to unravel the situation.
> I have a probit model with two independent variables and an interaction term between these two variables.
> Let's say Y X1 X2 X3 , where X3 = X1*X2
> What about their marginal effects? With mfx I obtain the mfx for X1 and X2, I do not consider the result obtained for X3.
> I use "inteff" command to compute the correct marginal effect of the interaction term?
> Or am I wrong?

Yes, an interaction effect between X1 and X2 means that the effect of
X1 changes when X2 changes and vice versa. So the idea that there is
one effect of X1 in this model is wrong, there is one effect of X1 for
each value of X2. Typically, in linear models one would look at the
effect of X1 at some meaningful value of X2 (either the mean or the
minimum or some other value that is of substantive interest) and look
at the interaction effect to see how much that effect changes when X2
changes. I am not sure if the same trick works that well with marginal
effects in non-linear models. I could imagine that they can be
approximately right, but I could also imagine situations where they
could be moderately or even horribly wrong. If you want to go that way
you will have to derive those results. Needless to say, I would not go
that way.

> and interaction effect is different from marginal effect of the interaction term, not just in the name?

It depends on the exact definition given to these terms, and they can
differ quite a bit from discipline to discipline and even from person
to person within a discipline, and sometimes  even within a person
over time. I would say that they are the same in a linear probability
model, but not so in non-linear model. There is also a direct relation
between these two if you use a -logit- model and the ratio
interpretation. In case of marginal effects it is good to remember
that they are simplifications of the model, and in models with
interactions the friction between the model and its simplified
representation can be considerable. I would say so considerable that
the simplification (=marginal effect) is no longer useful.

If both X1 and X2 are binary and (apart from the interaction term)
there are no other variables in your model, than you can without
problem do a linear probability model. In other situations, the
problem becomes a bit more tricky, but it may still work. In most
cases I would actually prefer the -logit- together with the ratio

-- Maarten

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
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