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st: Re: Stata tip 87: Interpretation of interactions in non-linear models

From   Maarten Buis <>
Subject   st: Re: Stata tip 87: Interpretation of interactions in non-linear models
Date   Tue, 17 May 2011 11:02:00 +0200

On Mon, May 16, 2011 at 3:52 PM,  andre ebner wrote:
> The only doubt I still have for the moment concerns the
> "marginal effect as the difference between the expected
> odds of women with and without a college degree, rather than as the
> derivative of the expected odds with respect to collgrad."
> as explained in your STATA tip 87.
> With my data the difference changes depending at which values I fix the
> other covariates. Is this due to the fact that we estimate marginal
> effects at certain values and marginal effects depend on these values? For
> calculating the impact of collgrade on black and white women would it then
> make sense to calculate the difference between average partial effects
> using
> margins , over(black collgrad) expression(exp(xb())) post
> also (or especially) if the regression includes additional covariates?
> Using my data, the differences are:
> * fixing covariates at certain value
>            inc_shock   no inc_shock    difference
> loan_const      0.21    0.02            0.19
> no loan_const   0.00    0.02           -0.02
> * fixing covariates at slightly different values
>            inc_shock   no inc_shock    difference
> loan_const      0.24    0.03            0.21
> no loan_const   0.00    0.02           -0.02
> * using margins, over(inc_shock loan_const)expression(exp(xb())) /// post
>            inc_shock   no inc_shock    difference
> loan_const      0.71    0.11            0.59
> no loan_const   0.02    0.08           -0.06
> You mention that without fixing the covariates one gets the odds averaged
> over the other control variables, while the logistic regression model is
> based on odds before averaging. Is it however possible to interprete the
> last table as kind of average partial effects (APE) over the odds of
> individuals showing the respective combination of inc_shock (=income
> shock) and loan_const (loan constrained). Would you agree to look at the
> last table if one is interested in differences between APEs?

In your case (with a panel model) this would be a mixture of average
partial effects while fixing the unobserved group constants at the
average. This is not very pretty, especially because the variability
of the individual partial effects for interaction effects is so high
that it really matters.

The problem with partial effects or marginal effects for interaction
effects is that they are very unstable. They tend to depend strongly
on the values of all explanatory variables, and it is perfectly normal
that for some observations you find a significant negative interaction
effect and for other observations you find a significant positive
effect. The computation of average partial or marginal effects only
makes sense if that average is a reasonable summary. My feeling is
that the variation is typically so large that the only way to
faithfully represent marginal or partial effects of interaction
effects is to compute them for each observation and just graph them,
just as Edward Norton, Hua Wang, and Chunrong Ai (2004) did. This is
where my suggestion (Buis 2010) for interpreting them as ratios of
odds ratios has an edge, the interaction effect is than really one

Hope this helps,

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

Edward Norton, Hua Wang, and Chunrong Ai (2004) "Computing interaction
effects and standard errors in logit and probit models" The Stata
Journal, 4(2):154--167.

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

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