Re: st: no difference between results obtained from -margins- and -margins, atmeans-

[Austin Nichols <austinnichols@gmail.com>]

Sarah <burgards@umich.edu>:
The -atmeans- distinction arises because f(E(xb)) is not equal to
E(f(xb)), in general.
But for linear regressions, f(E(xb)) does equal E(f(xb)), so atmeans
should have no impact.

I am using "linear" in slightly nonstandard way, however: a linear
model is linear in parameters,
but may have x and x^2 used as predictors, in which case a prediction
at E(x) is not nec.
the same as the mean prediction across observed values of x.

Do you mean to "take out" the contributions of covariates and show the
gender diff
at each age?  Note that interacting gender with all covariates ensures
they have
different impacts on different genders--see also -oaxaca- on SSC and
http://www.stata-journal.com/sjpdf.html?articlenum=st0151
showing how to say what part of an observed difference is due to
differences in covariates and what part is due to differences in coefs.

On Thu, Apr 12, 2012 at 10:39 AM, Burgard, Sarah <burgards@umich.edu> wrote:
> Dear colleagues,
> I have what is probably a simple question. I am exploring the implications of obtaining predictions using -margins- versus -margins, atmeans-  for simple weighted OLS regressions.
>
> My substantive goal is to obtain the "adjusted" or predicted gender difference in minutes of sleep across age categories, adjusting for a large number of covariates that predict sleep and including interactions between female gender and covariates. I believe that what I want is obtained by specifying -margins female, over(agecat)- after running the regression model.
>
> However, Stata 12 is returning the same predicted values for both -margins female, over(agecat)- and -margins female, over(agecat) atmeans-
>
> This happens when using a simpler model with the "auto" data that we are all familiar with as well - please see below. Does anyone see what I am doing wrong (note that I have the same problem even if I restimate the same model and then request -margins, atmeans-)
> thank you,
> Sarah Burgard
>
> . sysuse auto
> (1978 Automobile Data)
> . regress mpg turn i.foreign
>      Source |       SS       df       MS              Number of obs =      74
> -------------+------------------------------           F(  2,    71) =   38.97
>       Model |  1278.68109     2  639.340545           Prob > F      =  0.0000
>    Residual |  1164.77837    71  16.4053292           R-squared     =  0.5233
> -------------+------------------------------           Adj R-squared =  0.5099
>       Total |  2443.45946    73  33.4720474           Root MSE      =  4.0503
> ------------------------------------------------------------------------------
>         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>        turn |  -1.029205    .138914    -7.41   0.000    -1.306192   -.7522186
>   1.foreign |  -1.263614   1.328003    -0.95   0.345    -3.911577    1.384349
>       _cons |   62.47956   5.784252    10.80   0.000     50.94609    74.01303
> ------------------------------------------------------------------------------
> . margins foreign
>
> Predictive margins                                Number of obs   =         74
> Model VCE    : OLS
> Expression   : Linear prediction, predict()
> ------------------------------------------------------------------------------
>             |            Delta-method
>             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>     foreign |
>          0  |   21.67297   .6144672    35.27   0.000     20.46863     22.8773
>          1  |   20.40935   1.045246    19.53   0.000     18.36071      22.458
> ------------------------------------------------------------------------------
> . margins foreign, atmeans
>
> Adjusted predictions                              Number of obs   =         74
> Model VCE    : OLS
> Expression   : Linear prediction, predict()
> at           : turn            =    39.64865 (mean)
>               0.foreign       =    .7027027 (mean)
>               1.foreign       =    .2972973 (mean)
> ------------------------------------------------------------------------------
>             |            Delta-method
>             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>     foreign |
>          0  |   21.67297   .6144673    35.27   0.000     20.46863     22.8773
>          1  |   20.40935   1.045246    19.53   0.000     18.36071      22.458
> ------------------------------------------------------------------------------
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Sarah Burgard
> Associate Professor
> Sociology | Epidemiology | Population Studies Center
> University of Michigan
> http://sarahburgard.com/

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