Hello,

I'm wondering why margins (after logit) produces different results for a dummy variable (0-1) depending on whether the i-prefix is used or not. Estimates of coefficients of smoke are (logically) identical, but the marginal effect and standard error of smoke differ (0.1352669 vs.0.140626). See code and result below.

Thank you,
Mike


Code:
. webuse lbw
(Hosmer & Lemeshow data)

. logit low age lwt smoke

Iteration 0:   log likelihood =   -117.336  
Iteration 1:   log likelihood = -111.55075  
Iteration 2:   log likelihood = -111.44794  
Iteration 3:   log likelihood = -111.44776  
Iteration 4:   log likelihood = -111.44776  

Logistic regression                             Number of obs     =        189
                                                LR chi2(3)        =      11.78
                                                Prob > chi2       =     0.0082
Log likelihood = -111.44776                     Pseudo R2         =     0.0502

------------------------------------------------------------------------------
         low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |    -.03902   .0327243    -1.19   0.233    -.1031585    .0251184
         lwt |  -.0121153   .0061336    -1.98   0.048    -.0241368   -.0000938
       smoke |   .6706699   .3258659     2.06   0.040     .0319845    1.309355
       _cons |    1.36601   1.014251     1.35   0.178    -.6218848    3.353905
------------------------------------------------------------------------------

. margins, dydx(*)

Average marginal effects                        Number of obs     =        189
Model VCE    : OIM

Expression   : Pr(low), predict()
dy/dx w.r.t. : age lwt smoke

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0078699   .0065191    -1.21   0.227    -.0206472    .0049073
         lwt |  -.0024435   .0011968    -2.04   0.041    -.0047892   -.0000979
       smoke |   .1352669   .0630567     2.15   0.032     .0116781    .2588556
------------------------------------------------------------------------------

. logit low age lwt i.smoke

Iteration 0:   log likelihood =   -117.336  
Iteration 1:   log likelihood = -111.55075  
Iteration 2:   log likelihood = -111.44794  
Iteration 3:   log likelihood = -111.44776  
Iteration 4:   log likelihood = -111.44776  

Logistic regression                             Number of obs     =        189
                                                LR chi2(3)        =      11.78
                                                Prob > chi2       =     0.0082
Log likelihood = -111.44776                     Pseudo R2         =     0.0502

------------------------------------------------------------------------------
         low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |    -.03902   .0327243    -1.19   0.233    -.1031585    .0251184
         lwt |  -.0121153   .0061336    -1.98   0.048    -.0241368   -.0000938
             |
       smoke |
     smoker  |   .6706699   .3258659     2.06   0.040     .0319845    1.309355
       _cons |    1.36601   1.014251     1.35   0.178    -.6218848    3.353905
------------------------------------------------------------------------------

. margins, dydx(*)

Average marginal effects                        Number of obs     =        189
Model VCE    : OIM

Expression   : Pr(low), predict()
dy/dx w.r.t. : age lwt 1.smoke

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0078699   .0065191    -1.21   0.227    -.0206472    .0049073
         lwt |  -.0024435   .0011968    -2.04   0.041    -.0047892   -.0000979
             |
       smoke |
     smoker  |    .140626   .0688897     2.04   0.041     .0056047    .2756473
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.