Interpretation of Adjusted Predictions Contrasts (Margins command)

[Luc Meunier]

Dear Statalist,

I am new to the Margins command and would really appreciate some help with interpreting results.

I fitted a regression model comparing the Loss Aversion coefficient of participants. Independent variables include the sex of participants (1=Male), their Age, and their job (grouped in 3 categories, 0 / 1 / 2). Importantly, Group 1 is on average older and includes more men than the other groups.

. reg MeanLA i.Group##i.Man c.Age##c.Age, robust

Linear regression                               Number of obs     =        607
                                                F(7, 599)         =       7.43
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0535
                                                Root MSE          =     3.6296

------------------------------------------------------------------------------
             |               Robust
      MeanLA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       Group |
          1  |  -2.309667   1.239862    -1.86   0.063    -4.744672    .1253371
          2  |   .3365652   .5623473     0.60   0.550    -.7678468    1.440977
             |
       1.Man |  -2.174487   .5937994    -3.66   0.000    -3.340669   -1.008305
             |
   Group#Man |
        1 1  |   3.485428    1.34037     2.60   0.010      .853032    6.117823
        2 1  |   1.059777     .69054     1.53   0.125    -.2963965    2.415951
             |
         Age |  -.1975838   .1351799    -1.46   0.144     -.463068    .0679004
             |
 c.Age#c.Age |    .003306   .0016139     2.05   0.041     .0001363    .0064756
             |
       _cons |    7.02677   2.236967     3.14   0.002     2.633517    11.42002
------------------------------------------------------------------------------

We observe an interaction pattern in the regression: Job Group 1 * sex.

I thus used margins to obtain predictions for each pair of job group/ sex, that I understand in this case to be adjusted for Age (e.g., assuming everyone is 25.1, the mean of age here).

. margins Group#Man, atmeans

I then use margins again with contrasts to compare predictions for each group adjusted for Gender and Age (estimated to be at the mean for everyone).

. margins a.Group, atmeans

Contrasts of adjusted predictions
Model VCE    : Robust

Expression   : Linear prediction, predict()
at           : 0.Group         =    .1680395 (mean)
               1.Group         =    .0939044 (mean)
               2.Group         =     .738056 (mean)
               0.Man           =    .4777595 (mean)
               1.Man           =    .5222405 (mean)
               Age             =     25.1944 (mean)

------------------------------------------------
             |         df           F        P>F
-------------+----------------------------------
       Group |
   (0 vs 1)  |          1        0.28     0.5988
   (1 vs 2)  |          1        2.72     0.0997
      Joint  |          2        4.85     0.0082
             |
 Denominator |        599
------------------------------------------------

My interpretation of these results is that if we consider stereotypical groups (52.2% Man, 25.19 years old), group 1 would be significantly different from group 2 (marginally again, p = 10%). Is that the way this command works?

Thank you so much in advance!