margins + reg, nocons

[Luis Pecht]

Hi,

Does anyone knows, conceptually, why nocons affects margins calculations?

. webuse auto, clear
(1978 automobile data)

. reg price mpg i.foreign,nocons

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 72)        =     73.73
       Model |  2.3167e+09         2  1.1583e+09   Prob > F        =    0.0000
    Residual |  1.1311e+09        72  15710259.5   R-squared       =    0.6719
-------------+----------------------------------   Adj R-squared   =    0.6628
       Total |  3.4478e+09        74  46592355.7   Root MSE        =    3963.6

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |   251.1707   26.42008     9.51   0.000     198.5032    303.8382
             |
     foreign |
    Foreign  |   162.4989   1068.864     0.15   0.880    -1968.242     2293.24
------------------------------------------------------------------------------

. margins ,at(mpg=(5500(250)6751)) atmeans

Adjusted predictions                                        Number of obs = 74
Model VCE: OLS

Expression: Linear prediction, predict()
...
6._at: mpg       =     6750
       0.foreign = .7027027 (mean)
       1.foreign = .2972973 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         _at |
          1  |          .  (not estimable)
          2  |          .  (not estimable)
          3  |          .  (not estimable)
          4  |          .  (not estimable)
          5  |          .  (not estimable)
          6  |          .  (not estimable)
------------------------------------------------------------------------------


. reg price mpg i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     14.07
       Model |   180261702         2  90130850.8   Prob > F        =    0.0000
    Residual |   454803695        71  6405685.84   R-squared       =    0.2838
-------------+----------------------------------   Adj R-squared   =    0.2637
       Total |   635065396        73  8699525.97   Root MSE        =    2530.9

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -294.1955   55.69172    -5.28   0.000    -405.2417   -183.1494
             |
     foreign |
    Foreign  |   1767.292    700.158     2.52   0.014     371.2169    3163.368
       _cons |   11905.42   1158.634    10.28   0.000     9595.164    14215.67
------------------------------------------------------------------------------

. margins ,at(mpg=(5500(250)6751)) atmeans

Adjusted predictions                                        Number of obs = 74
Model VCE: OLS

Expression: Linear prediction, predict()
...
6._at: mpg       =     6750
       0.foreign = .7027027 (mean)
       1.foreign = .2972973 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   -1605645   305118.5    -5.26   0.000     -2214034   -997255.6
          2  |   -1679193   319041.4    -5.26   0.000     -2315344    -1043043
          3  |   -1752742   332964.4    -5.26   0.000     -2416654    -1088830
          4  |   -1826291   346887.3    -5.26   0.000     -2517965    -1134618
          5  |   -1899840   360810.2    -5.27   0.000     -2619275    -1180405
          6  |   -1973389   374733.1    -5.27   0.000     -2720586    -1226192
------------------------------------------------------------------------------

thanks.

[Clyde Schechter]

The problem is that you specified i.foreign and -nocons- together. This left the model with no way to account for foreign = 0 observations. Consequently when -margins- encounters those, it doesn't know what to do and concludes that what you are asking for cannot be calculated.

You need to account for the 0 level of foreign in your model somehow. Normally, the constant term does that. Without that, you need to include an indicator ("dummy") variable for it.

sysuse auto, clear

reg price mpg ibn.foreign, nocons

margins, at(mpg = (5500(250)6751)) atmeans

You will note that this gives you the same results as -margins- after -reg price mpg i.foreign- (without -nocons-).

[Rich Goldstein]

a slight amendment - you should use the "hascons" option rather than the "nocons" option (since the two terms for foreign sum to a constant); this will not affect -margins- but will affect the regression summary statistics such as R²