marginal effects after probit and xtprobit

[Christina Chara]

I am running static and dynamic versions of both pooled probit(

probit depvar indepvar, robust

)and panel probit models (

xtprobit depvar indepvar, vce(cluster id)

) and I am puzzled as to what is the correct average marginal effects command I should use in postestimation. I have tried both

margins, dydx(*)

and

margins, predict(pu0) dydx(*)

and I get very different marginal effects both in terms of coefficients and in terms of the statistical significance of my variables. More specifically, when I use the linear margins, dydx(*) command, I get significant results for most of my explanatory variables, yet only 1 or 2 are significant when I use the predict(pu0) option.
Lastly, when I try to use

margins, predict(pu0) dydx(*)

after the pooled probit model

probit

Stata gives me the following error

option pu0 not allowed
r(198);

Is the predict option in the margins only for panel probit specifications and does this mean I should use margins,dydx(*) after the cross sectional probit but margins, predict(pu0) dydx(*) after the panel probit?

Any insight would be greatly appreciated as I haven't been able to find a clear answer in the literature.

[Richard Williams]

Is the predict option in the margins only for panel probit specifications and does this mean I should use margins,dydx(*) after the cross sectional probit but margins, predict(pu0) dydx(*) after the panel probit?

pu0 is used after xtprobit but not probit. pu0 calculates the probability of a positive outcome, assuming that the random effect for that observation's panel is zero.

margins,dydx(*) after the cross sectional probit has the same effect as specifying predict(p), i.e. probabilities are the default. In xtprobit, xb is the default.

I would do things the way you suggest.

[Christina Chara]

this is indeed very helpful. I will follow your advice. thank you very much

[Sasha Gulabivala]

Is there a way to test the assumption that:

the random effect for that observation's panel is zero

I am running

xtprobit, re vce(cluster id)

and think that:

margins, dydx(*) predict(pu0)

should be used instead of the default xb (which actually returns marginal effects that are identical to the coefficients in my regression):

margins, dydx(*)

but I would like to know how to justify this? Many thanks

[Richard Williams]

This discussion, especially Steve Samuel's comments, may be helpful.

http://www.statalist.org/forums/foru...-after-xtlogit

[Sasha Gulabivala]

Thank you for the link - it is making it easier to understand.

I also found your posts here relevant: http://www.statalist.org/forums/foru...after-xtprobit
I also went through the handouts, especially the sections on Average Marginal Effects, where you use margins, dydx(*) as it is a logit/probit and not an xtlogit/xtprobit model.

I am using xtprobit,re and I would like to ask why you recommend pu0 with xtprobit? I read your post that it uses

predicted probabilities rather than the linear prediction

but I wondered why this is better for xtprobit?

[Sasha Gulabivala]

Hi,

So my understanding is that the margins, dydx(*) uses xb as a default, and this uses a linear prediction.
Furthermore, margins, dydx(*) predict pu0 uses predicted probabilities.
I believe that neither of these achieve the marginal effects that I want.

I did some further research into the CRE Probit Model (Chamberlain-Mundlak) that I am using and the following post (http://www.statalist.org/forums/foru...14#post1349614) recommended computing the marginal effects with the following command:

margins, expression(normalden(xb()*(1/sqrt(1 + e(sigma_u)^2)))*(_b[kids])*(1/sqrt(1 + e(sigma_u)^2))) force

Is the code above appropriate for my model because, instead of linear prediction or predicted probabilities, it imposes the following change on the density function?

normalden(xb()*(1/sqrt(1 + e(sigma_u)^2)))

Thanks

[Ariel Karlinsky]

... In xtprobit, xb is the default.

Actually, according to the help file and a quick test I ran, after xtprobit, the default in margins is pr.

[Richard Williams]

Actually, according to the help file and a quick test I ran, after xtprobit, the default in margins is pr.

I wrote my comment more than 2 years ago. In Stata 13 xb was the default, but in 14 it is pr. 14 does a much better job of documenting what margins does after each command than 13 did.

You can see margins exhibiting the old behavior if you do something like

version 13.1: margins, dydx(*)

[Ariel Karlinsky]

Oh, sorry for the bump then! I saw Sasha's comment and thought this was a discussion from 2017...

[Richard Williams]

No need to apologize! Not everyone uses the latest and greatest version of Stata. so it is good to know that behavior varies. Also, people often don't realize what option margins is using, e.g. we have often had people ask "why am I getting negative predicted probabilities" when what they were really getting was xb. Stata 14 has better documentation but even without it, if you look carefully at the margins output you can see what option margins was using.