What's exactly the grand mean used by "margins gw." command?

[JL Martinez-Cantos]

Hello,
This is my first post here in the forum, but I have frequently visited this forum. Very useful information here, thank you!
I have a very specific question: What's exactly the grand mean used by "margins gw." command?
I find that, after logit regression (see and example below), the differences between levels of a factor variable (e.g. "race") are the same with "margins" and "margins gw.":

webuse nhanes2f, clear
logit diabetes i.female weight height i.race
margins race, grand
margins gw.race

However, the considered grand mean is not the same. Why "margins gw." doesn't use the grand mean given by "margins"?

[Marcos Almeida]

Welcome to the Stata Forum/Statalist,

"gw" is for difference from the weighted grand mean whereas "g" is for difference from the balanced grand mean.

[JL Martinez-Cantos]

Thank you so much for your answer, Marcos Almeida. My question is not about the difference between "gw" and "g" grand means, but about the difference between "gw" grand mean and "margins" grand mean. Is the "margins" grand mean a weighted one?

Let's go back to my example:

webuse nhanes2f, clear
logit diabetes i.female weight height i.race
margins race, grand

The last command returns a grand mean = .0482825. Running "margins, dydx(race)" returns the same results as manually calculating the differences between the predictive "margins" for each group minus that grand mean. However,

margins gw.race

does not return the same results in its contrasts of predictive margins and the implicit* (weighted) grand mean would be .0480315 [*assuming that predictive margins and marginal effects are always the same].

So, again, why are those margin coefficients and grand means different?

[Marcos Almeida]

In the example below, we can get these results:

. sysuse auto
(1978 Automobile Data)

. gen highmpg = mpg > 21

. quiet: logit foreign price weight i.highmpg

. margins highmpg, grand

Predictive margins                              Number of obs     =         74
Model VCE    : OIM

Expression   : Pr(foreign), predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     highmpg |
          0  |   .3963082   .0367545    10.78   0.000     .3242708    .4683456
          1  |   .2327371   .0377345     6.17   0.000      .158779    .3066953
             |
       _cons |   .2972973   .0300242     9.90   0.000      .238451    .3561436
------------------------------------------------------------------------------

. di 0.3963082 - 0.2327371
.1635711

. margins gw.highmpg

Contrasts of predictive margins
Model VCE    : OIM

Expression   : Pr(foreign), predict()

------------------------------------------------
             |         df        chi2     P>chi2
-------------+----------------------------------
     highmpg |
(0 vs mean)  |          1        8.32     0.0039
(1 vs mean)  |          1        8.32     0.0039
      Joint  |          1        8.32     0.0039
------------------------------------------------

--------------------------------------------------------------
             |            Delta-method
             |   Contrast   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
     highmpg |
(0 vs mean)  |    .068523   .0237621      .0219501    .1150959
(1 vs mean)  |   -.095048   .0329603     -.1596491    -.030447
--------------------------------------------------------------

. di 0.068523 - (-0.095048)
.163571

[JL Martinez-Cantos]

Thank you again, Marcos Almeida.
What you calculated in your example are the marginal effects between categories or levels and, yes, they are the same in both "margins, grand" and "margins gw.". I am not talking about those effects but about the marginal effects with respect to the grand means in each case, meaning that the issue is focused on the grand means. So, in your example, my questions would be:
-> Why "di .3963082 - .2972973" [i.e. predictive margin of '0' minus 'population averaged' grand mean] returns a different result (= .0990109) than the contrast "0 vs mean" [i.e. marginal effect of '0' minus 'weighted observed' grand mean] does (= .068523)?
-> If the grand means are different, why and how can each one be defined?