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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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 interpretation. -- Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: inteff and mfx?***From:*Luca Fumarco <luca.fumarco@lnu.se>

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