Probit marginal effects

[Helder Costa]

Hello,
I'm running the following code:

webuse nhanes2d, clear

probit highbp weight age age2 i.female##c.height loglead i.sizplace
    est store e2
    
margins, dydx(female)    

sum height    
margins , dydx(female) at(height = `r(mean)')

margins , dydx(female) atmeans

However, the result for the first marginal effect is .0413987, for the second is -.0409966 and third is .5251667. Up to this point, I thought that when using

margins, dydx(female)

, it would compute at the mean, so I would expect that the last margins command would yield the same as the first.

What am I missing?
Thank you for your time!

Hélder Costa

[Clyde Schechter]

No, your understanding of how -margins- works is incorrect.

-margins, dydx(female)- computes an average marginal effect. This is not the marginal effect at the mean value(s) of anything. In fact, it takes all of the values of the explanatory variables, except female, from the regression at their existing values--it does not involve the means of any of them. It is the difference between the overall predicted probability if everyone were female and the overall predicted probability if everyone were male, given all of the other explanatory variables as they are.

-margins, dydx(female) at (height = `r(mean)-)- is similar, except that before the calculations are done, the variable height is replaced by its mean value in every observation.

-margins, dydx(female) atmeans- takes us even farther from the first -margins- command. In this case, all of the explanatory variables are replaced by their mean values, and then the difference between the overall predicted probability if everyone were female and the overall predicted probability if everyone were male. Added: This one is sometimes called the "marginal effect at the means." Note that this is not the same as "average marginal effect."

So, as you can see, these are all very different things. They are answers to different questions. Which one is appropriate for your use depends on what question you are trying to answer.

[Helder Costa]

Thank you Clyde Schechter, your answer was very helpful!