Post-estimation command

Stata “estimation” commands are primarily those which fit models.
- E.g. regress, logit, mixed, xtreg.
Stata “stores” the most recent estimation command.
margins is a post-estimation command; meaning it will use the most recently run estimation.
margins itself is not an estimation command.

Categorical variables

. sysuse nlsw88
(NLSW, 1988 extract)

. list in 1

     +----------------------------------------------------------------+
  1. | idcode | age  |  race  | married  |    never_married  | grade  |
     |      1 |  37  | Black  |  Single  | Has been married  |    12  |
     |----------------------------------------------------------------|
     |          collgrad  |      south  |  smsa  |            c_city  |
     |  Not college grad  |  Not south  |  SMSA  |  Not central city  |
     |----------------------------------------------------------------|
     |               industry | occupation | union |     wage | hours |
     | Transport/Comm/Utility | Operatives | Union | 11.73913 |    48 |
     |----------------------------------------------------------------|
     |            ttl_exp            |              tenure            |
     |           10.33333            |            5.333333            |
     +----------------------------------------------------------------+

Fitting the model

. regress wage i.race

      Source |       SS           df       MS      Number of obs   =     2,246
-------------+----------------------------------   F(2, 2243)      =     10.28
       Model |  675.510282         2  337.755141   Prob > F        =    0.0000
    Residual |  73692.4571     2,243  32.8544169   R-squared       =    0.0091
-------------+----------------------------------   Adj R-squared   =    0.0082
       Total |  74367.9674     2,245  33.1260434   Root MSE        =    5.7319

------------------------------------------------------------------------------
        wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        race |
      Black  |  -1.238442   .2764488    -4.48   0.000    -1.780564   -.6963193
      Other  |   .4677818   1.133005     0.41   0.680    -1.754067    2.689631
             |
       _cons |   8.082999   .1416683    57.06   0.000     7.805185    8.360814
------------------------------------------------------------------------------

Group	Average	Comparison	Diff. in Averages
White	8.083	White vs Black	-1.238
Black	???	White vs Other	0.468
Other	???	Black vs Other	???

Calculating group effects and comparisons

. regress, noheader
------------------------------------------------------------------------------
        wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        race |
      Black  |  -1.238442   .2764488    -4.48   0.000    -1.780564   -.6963193
      Other  |   .4677818   1.133005     0.41   0.680    -1.754067    2.689631
             |
       _cons |   8.082999   .1416683    57.06   0.000     7.805185    8.360814
------------------------------------------------------------------------------

\[ wage = \beta_0 + \beta_1\textrm{Black} + \beta_2\textrm{Other} + \epsilon \]

Group	Average
White	8.083
Black	8.083 + -1.238 = 6.845
Other	8.083 + 0.468 = 8.551

Comparison	Diff. in Averages
White vs Black	-1.238
White vs Other	0.468
Black vs Other	0.468 - -1.238 = 1.706

Changing reference category

. regress wage ib2.race, noheader
------------------------------------------------------------------------------
        wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        race |
      White  |   1.238442   .2764488     4.48   0.000     .6963193    1.780564
      Other  |   1.706223   1.148906     1.49   0.138    -.5468071    3.959254
             |
       _cons |   6.844558   .2373901    28.83   0.000     6.379031    7.310085
------------------------------------------------------------------------------

. regress wage ib3.race, noheader
------------------------------------------------------------------------------
        wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        race |
      White  |  -.4677818   1.133005    -0.41   0.680    -2.689631    1.754067
      Black  |  -1.706223   1.148906    -1.49   0.138    -3.959254    .5468071
             |
       _cons |   8.550781   1.124114     7.61   0.000      6.34637    10.75519
------------------------------------------------------------------------------

Estimated means

margins does this for us!

Group	Average
White	8.083
Black	8.083 + -1.238 = 6.845
Other	8.083 + 0.468 = 8.551

. margins race

Adjusted predictions                                     Number of obs = 2,246
Model VCE: OLS

Expression: Linear prediction, predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        race |
      White  |   8.082999   .1416683    57.06   0.000     7.805185    8.360814
      Black  |   6.844558   .2373901    28.83   0.000     6.379031    7.310085
      Other  |   8.550781   1.124114     7.61   0.000      6.34637    10.75519
------------------------------------------------------------------------------

Differences in estimated means

Comparison	Diff. In Averages
White vs Black	-1.238
White vs Other	0.468
Black vs Other	0.468 - -1.238 = 1.706

. margins race, pwcompare

Pairwise comparisons of adjusted predictions             Number of obs = 2,246
Model VCE: OLS

Expression: Linear prediction, predict()

-----------------------------------------------------------------
                |            Delta-method         Unadjusted
                |   Contrast   std. err.     [95% conf. interval]
----------------+------------------------------------------------
           race |
Black vs White  |  -1.238442   .2764488     -1.780564   -.6963193
Other vs White  |   .4677818   1.133005     -1.754067    2.689631
Other vs Black  |   1.706223   1.148906     -.5468071    3.959254
-----------------------------------------------------------------

Syntax for estimated means

Average outcome per level

margins [categorical variable]

Pairwise comparisons between groups

margins [categorical variable], pwcompare(ci) // Produce confidence intervals, default
margins [categorical variable], pwcompare(pv) // Produce p-values

Do not preface the categorical variable with i..
In general, binary (0/1) variables can be treated as continuous or categorical in the model. The model is identical either way, but treating them as categorical lets margins operate in this easy fashion.

In the presence of covariates

. regress wage age i.married, noheader
------------------------------------------------------------------------------
        wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |  -.0692705   .0396596    -1.75   0.081     -.147044    .0085029
             |
     married |
    Married  |  -.4958806   .2530888    -1.96   0.050    -.9921934    .0004321
       _cons |   10.79748   1.568569     6.88   0.000     7.721481    13.87348
------------------------------------------------------------------------------

. margins married

Predictive margins                                       Number of obs = 2,246
Model VCE: OLS

Expression: Linear prediction, predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     married |
     Single  |   8.085319   .2027826    39.87   0.000     7.687658    8.482981
    Married  |   7.589439    .151412    50.12   0.000     7.292517    7.886361
------------------------------------------------------------------------------

Visualization of `margins`

margins married

Stata’s margins command

Post-estimation command

Categorical variables

Fitting the model

Calculating group effects and comparisons

Changing reference category

Estimated means

Differences in estimated means

Syntax for estimated means

In the presence of covariates

Visualization of margins

Stata’s `margins` command

Visualization of `margins`