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Margins after meprobit

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Hi everyone,

I'm using meprobit to estimate a random effects panel probit model because I had issues trying to do xtprobit. I now have a concern with margins estimation after meprobit. Consider the following example I have prepared:
:
clear all
set more off

use "http://www.ats.ucla.edu/stat/data/hsbdemo"

xtset cid
global vars "honors read i.female"
xtprobit $vars
margins, dydx(read)
meprobit $vars || cid:, intpoint(12)
margins, dydx(read) predict(mu fixedonly)
xtprobit estimation:

Array
xtprobit margins:

Array
meprobit estimation:

Array
meprobit margins:

Array

So we see the estimations' results are identical, as expected, but as we get to the margins there is a huge difference. My question is whether this is because of the random effects? If so... why? Notice that read only enters the fixed part of the meprobit specification. Why, then, should the group randomness affect the marginal effect that read has on the probability of honors=1? Then if assuming that the margins estimation after xtprobit is the right one, how do I replicate it after meprobit?

Any help is really appreciated!!!! Thanks.

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