Difference between at() and over() in a non-interacted margins command.

[David Speed]

Hi Everyone,

I'm running a survey-weighted regression model with marginal means estimates. I noticed that over() and at() do not produce equivalent results and I was unsure why. Here's the relevant portion of the regression output. There were no interaction terms and there were a dozen covariates.

       relid |

------------------------------------------------------------------------------
             |             Linearized
          dv |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------

       relid |
  Agnostics  |  -.2154432   .0940226    -2.29   0.022    -.3998531   -.0310333
 OtherNones  |   -.244422   .1706986    -1.43   0.152    -.5792192    .0903751
       NIPs  |  -.2634163   .0966674    -2.72   0.006    -.4530134   -.0738191
Protestants  |  -.5831272   .0987427    -5.91   0.000    -.7767946   -.3894598
  Catholics  |  -.4672434   .0953257    -4.90   0.000    -.6542089   -.2802779
 Christians  |  -.3771565    .182936    -2.06   0.039    -.7359551   -.0183579

When I ran the margins command initially it was:

margins, at(relid = (0 1 2 3 4 5 6)) atmeans pwcomp(pv)
-----------------------------------------------------
             |            Delta-method    Unadjusted
             |   Contrast   Std. Err.      t    P>|t|
-------------+---------------------------------------
         _at |
     2 vs 1  |  -.2154432   .0940226    -2.29   0.022
     3 vs 1  |   -.244422   .1706986    -1.43   0.152
     4 vs 1  |  -.2634163   .0966674    -2.72   0.006
     5 vs 1  |  -.5831272   .0987427    -5.91   0.000
     6 vs 1  |  -.4672434   .0953257    -4.90   0.000

By happenstance I happened to enter a different margins specification the next time I ran the model, and got different results

margins, over(relid) atmeans pwcomp(pv)
-------------------------------------------------------------------
                           |            Delta-method    Unadjusted
                           |   Contrast   Std. Err.      t    P>|t|
---------------------------+---------------------------------------
                     relid |
    Agnostics vs Atheists  |  -.2330303   .0940864    -2.48   0.013
   OtherNones vs Atheists  |  -.5501877   .1735495    -3.17   0.002
         NIPs vs Atheists  |  -.5491664   .0929277    -5.91   0.000
  Protestants vs Atheists  |  -1.014815   .0815914   -12.44   0.000
    Catholics vs Atheists  |  -.8043829   .0848022    -9.49   0.000
   Christians vs Atheists  |  -.8228742   .1765394    -4.66   0.000

I was curious why these did not produce the same estimates. relid was not interacted with anything and both models used the <atmeans> option. Could someone clarify what I am missing here?

Thanks!

David.

[Leonardo Guizzetti]

At will set each covariate for all observations in the subpopulation to that value, then compute the marginal means.

Over will instead compute estimates for each subgroup in the subpopulation.