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Note: This FAQ is for Stata 10 and older versions of Stata. In Stata 11, the margins command replaced mfx.

I need to run mfx more than once on my dataset, and it's taking a long time. What can I do to make it run as fast as possible?

Title   Obtaining marginal effects quickly
Author May Boggess, StataCorp
Date April 2004; minor revisions Sept 2005

First, do not compute the marginal effects for all the variables if you are not interested in all of them. You can specify the variables you are interested in by using the varlist() option.

 . sysuse auto, clear
 (1978 Automobile Data)

 . regress mpg weight length

       Source |       SS       df       MS              Number of obs =      74
 -------------+------------------------------           F(  2,    71) =   69.34
        Model |  1616.08062     2  808.040312           Prob > F      =  0.0000
     Residual |  827.378835    71   11.653223           R-squared     =  0.6614
 -------------+------------------------------           Adj R-squared =  0.6519
        Total |  2443.45946    73  33.4720474           Root MSE      =  3.4137
 
 ------------------------------------------------------------------------------
          mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
       weight |  -.0038515    .001586    -2.43   0.018    -.0070138   -.0006891
       length |  -.0795935   .0553577    -1.44   0.155    -.1899736    .0307867
        _cons |   47.88487    6.08787     7.87   0.000       35.746    60.02374
 ------------------------------------------------------------------------------

 . mfx, predict(xb) eyex

 Elasticities after regress
       y  = Linear prediction (predict, xb)
          =  21.297297
 ------------------------------------------------------------------------------
 variable |      ey/ex    Std. Err.     z    P>|z|  [    95% C.I.   ]      X
 ---------+--------------------------------------------------------------------
   weight |  -.5460497      .22509   -2.43   0.015  -.987208 -.104891   3019.46
   length |  -.7023518      .48867   -1.44   0.151  -1.66012  .255414   187.932
------------------------------------------------------------------------------

 . mfx, predict(xb) eyex varlist(length)

 Elasticities after regress
       y  = Linear prediction (predict, xb)
          =  21.297297
 ------------------------------------------------------------------------------
 variable |      ey/ex    Std. Err.     z    P>|z|  [    95% C.I.   ]      X
 ---------+--------------------------------------------------------------------
   length |  -.7023518      .48867   -1.44   0.151  -1.66012  .255414   187.932
 ------------------------------------------------------------------------------

Also, if you don’t need them, do not compute the standard errors as this can be time consuming. You achieve this with the nose option.

 . mfx, predict(xb) eyex nose

 Elasticities after regress
       y  = Linear prediction (predict, xb)
          =  21.297297
  -------------------------------------------------------------------------------
                         variable |          ey/ex                 X
 ---------------------------------+---------------------------------------------
                           weight |       -.5460497            3019.46
                           length |       -.7023518            187.932
 -------------------------------------------------------------------------------

The third thing you can do is use the force option. This prevents mfx from doing some checks that really should be done at least once. This will not save a noticeable amount of time on a small dataset but may save a few seconds on a large dataset. Here is an example you can run to compare:

 . clear
       
 . set obs 1000
  obs was 0, now 1000
             
 . set seed 23865
    
 . generate y=int(uniform()*5)
    
 . generate dum=uniform()>0.5
    
 . forvalues i=1/3 {
   2. generate x`i'=uniform()*20
   3. }
 
 . mlogit y x* dum, nolog
    
    
 Multinomial logistic regression                   Number of obs   =       1000
                                                   LR chi2(16)     =      16.56
                                                   Prob > chi2     =     0.4145
 Log likelihood = -1599.4028                       Pseudo R2       =     0.0052
    
 ------------------------------------------------------------------------------
            y |      Coef.   Std. Err.      z    p>|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 0            |
           x1 |  -.0018747   .0173475    -0.11   0.914    -.0358752    .0321257
           x2 |  -.0317412   .0178107    -1.78   0.075    -.0666495    .0031671
           x3 |   .0078188   .0174158     0.45   0.653    -.0263155    .0419532
          dum |   .1263877   .2021265     0.63   0.532     -.269773    .5225484
        _cons |   .0561327   .3304511     0.17   0.865    -.5915396     .703805
 -------------+----------------------------------------------------------------
 2            |
           x1 |   .0008903   .0172058     0.05   0.959    -.0328323     .034613
           x2 |  -.0027325   .0176622    -0.15   0.877    -.0373498    .0318849
           x3 |  -.0162843   .0173379    -0.94   0.348     -.050266    .0176974
          dum |   .0784832   .2000959     0.39   0.695    -.3136975     .470664
        _cons |   .0107956   .3299801     0.03   0.974    -.6359536    .6575447
 -------------+----------------------------------------------------------------
 3            |
           x1 |  -.0152809   .0167811    -0.91   0.363    -.0481712    .0176094
           x2 |    -.02041   .0171957    -1.19   0.235     -.054113     .013293
           x3 |   -.003969   .0168479    -0.24   0.814    -.0369902    .0290522
          dum |   .1989654   .1952902     1.02   0.308    -.1837963    .5817271
        _cons |   .2797189   .3186474     0.88   0.380    -.3448184    .9042563
 -------------+----------------------------------------------------------------
 4            |
           x1 |   .0163031   .0168514     0.97   0.333     -.016725    .0493312
           x2 |  -.0270747   .0172928    -1.57   0.117     -.060968    .0068186
           x3 |   .0202191   .0169027     1.20   0.232    -.0129096    .0533477
          dum |  -.1317624   .1965608    -0.67   0.503    -.5170144    .2534897
        _cons |  -.0551544   .3244424    -0.17   0.865    -.6910499    .5807411

 ------------------------------------------------------------------------------
 (y==1 is the base outcome)
     
 . mfx, predict(p outcome(2))    
     
 Marginal effects after mlogit
       y  = Pr(y==2) (predict, p outcome(2))
          =  .18900063
 ------------------------------------------------------------------------------
 variable |      dy/dx    Std. Err.     z    p>|z|  [    95% C.I.   ]      X
 ---------+--------------------------------------------------------------------
       x1 |    .000176      .00213    0.08   0.934  -.004008  .004359    9.9926
       x2 |   .0025355      .00218    1.16   0.246  -.001744  .006815   10.2813
       x3 |  -.0033915      .00215   -1.58   0.114  -.007602  .000819   9.44558
      dum*|   .0048542      .02479    0.20   0.845  -.043738  .053446      .496
 
 ------------------------------------------------------------------------------
 (*) dy/dx is for discrete change of dummy variable from 0 to 1
     
 . mfx, predict(p outcome(2)) force 

 Marginal effects after mlogit
       y  =  (predict, p outcome(2))
          =  .18900063
 ------------------------------------------------------------------------------
 variable |      dy/dx    Std. Err.     z    p>|z|  [    95% C.I.   ]      X
 ---------+--------------------------------------------------------------------
       x1 |    .000176      .00213    0.08   0.934  -.004008  .004359    9.9926
       x2 |   .0025355      .00218    1.16   0.246  -.001744  .006815   10.2813
       x3 |  -.0033915      .00215   -1.58   0.114  -.007602  .000819   9.44558
      dum*|   .0048542      .02479    0.20   0.845  -.043738  .053446      .496
 ------------------------------------------------------------------------------
 (*) dy/dx is for discrete change of dummy variable from 0 to 1

The command set rmsg on tells Stata to show us the amount of time taken on the previous command. If you use that command before mfx, Stata will tell you how long mfx took after it is done. On my computer, it took close to the same time with force as without. Use set rmsg off when you are done looking at times.

Please let me stress here that you should not get in the habit of using force all the time. The checks that force avoids are very, very important because, if any of those checks fail, the results are probably invalid. So, remember, use force only if you have previously run mfx without force and verified that everything checks out OK.

You may be tempted to use the at() option to try and save time. It’s not a bad idea since mfx won’t have to compute the means of the variables, but it won’t save a noticeable amount of time either, unless your dataset is very large. Let’s compare:

 . clear
     
 . set obs 10000
 obs was 0, now 10000
  
 . set seed 23865
  
 . generate y=int(uniform()*5)
     
 . forvalues i=1/3 {
   2. generate x`i'=uniform()*20
   3. }
  
 . quietly mlogit y x* 
     
 . forvalues i=1/3 {
   2. quietly summarize x`i' if e(sample)
   3. local xmean`i'=r(mean)
   4. }
  
 . mfx, predict(p outcome(2)) 
     
 Marginal effects after mlogit
       y  = Pr(y==2) (predict, p outcome(2))
          =  .18965252
 ------------------------------------------------------------------------------
 variable |      dy/dx    Std. Err.     z    P>|z|  [    95% C.I.   ]      X
 ---------+--------------------------------------------------------------------
       x1 |  -.0008298      .00218   -0.38   0.703  -.005096  .003436   9.96244
       x2 |     .00021      .00214    0.10   0.922  -.003975  .004395    9.9926
       x3 |   .0025351      .00219    1.16   0.247  -.001759  .006829   10.2813
 ------------------------------------------------------------------------------

 . mfx, predict(p outcome(2)) at(x1=`xmean1' x2=`xmean2' x3=`xmean3')  
     
  Marginal effects after mlogit
        y  = Pr(y==2) (predict, p outcome(2))
           =  .18965252
  ------------------------------------------------------------------------------
  variable |      dy/dx    Std. Err.     z    P>|z|  [    95% C.I.   ]      X
  ---------+--------------------------------------------------------------------
        x1 |  -.0008298      .00218   -0.38   0.703  -.005096  .003436   9.96244
        x2 |     .00021      .00214    0.10   0.922  -.003975  .004395    9.9926
        x3 |   .0025351      .00219    1.16   0.247  -.001759  .006829   10.2813
  ------------------------------------------------------------------------------
     
  . mfx, predict(p outcome(2)) at(x1=`xmean1' x2=`xmean2' x3=`xmean3')  force
     
  Marginal effects after mlogit
        y  =  (predict, p outcome(2))
           =  .18965252
  ------------------------------------------------------------------------------
  variable |      dy/dx    Std. Err.     z    P>|z|  [    95% C.I.   ]      X
  ---------+--------------------------------------------------------------------
        x1 |  -.0008298      .00218   -0.38   0.703  -.005096  .003436   9.96244
        x2 |     .00021      .00214    0.10   0.922  -.003975  .004395    9.9926
        x3 |   .0025351      .00219    1.16   0.247  -.001759  .006829   10.2813
  ------------------------------------------------------------------------------

The last thing you can do to save time is to verify that your variables are well scaled. (Please see the FAQ stata.com/support/faqs/statistics/scaling-and-marginal-effects for a full discussion of scaling.) If mfx is taking a long time, you can check whether a lot of iterations are slowing down the process by using the tracelvl() option, as follows:

 . webuse ldose, clear

 . glm r ldose, family(binomial n) link(clog)

 Iteration 0:   log likelihood = -14.883594  
 Iteration 1:   log likelihood = -14.822264  
 Iteration 2:   log likelihood = -14.822228  
 Iteration 3:   log likelihood = -14.822228  
  
 Generalized linear models                          No. of obs      =         8
 Optimization     : ML                              Residual df     =         6
                                                    Scale parameter =         1
 Deviance         =  3.446418004                    (1/df) Deviance =   .574403
 Pearson          =  3.294675153                    (1/df) Pearson  =  .5491125
 
 Variance function: V(u) = u*(1-u/n)                [Binomial]
 Link function    : g(u) = ln(-ln(1-u/n))           [Complementary log-log]

                                                    AIC             =  4.205557
 Log likelihood   = -14.82222811                    BIC             = -9.030231

 ------------------------------------------------------------------------------
              |                 OIM
            r |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
        ldose |   22.04118   1.793089    12.29   0.000     18.52679    25.55557
        _cons |  -39.57232   3.229047   -12.26   0.000    -45.90114   -33.24351
 ------------------------------------------------------------------------------
  
 . mfx, predict(xb) trace(4)
  
 calculating dydx (linear method)

 equation i= 1 
 Iteration (dx): initial h = 1.793e-06
 1  h= 1.345e-06
 2  h= 1.009e-06
 3  h= 7.566e-07
 4  h= 5.675e-07
 5  h= 4.256e-07
 6  h= 3.192e-07
 7  h= 2.394e-07
 8  h= 1.795e-07
 9  h= 1.347e-07
 10  h= 1.010e-07
 11  h= 7.575e-08
 12  h= 5.681e-08
 13  h= 4.261e-08
 14  h= 3.196e-08
 15  h= 2.397e-08
 16  h= 1.797e-08
 17  h= 1.348e-08
 18  h= 1.011e-08
 19  h= 7.583e-09
 20  h= 5.687e-09
 21  h= 4.266e-09
 22  h= 3.199e-09
 23  h= 2.399e-09
 24  h= 1.800e-09
 h= 1.800e-09
 : df/d(xb) = 1
 
 -------------------------
 variable |      dy/dx
 ---------+---------------
    ldose |       22.041
 -------------------------


 calculating standard errors (linear method)
 
 equation k = 1: 
 
 Iteration (dx): initial h = 1.793e-06
 1  h= 1.345e-06
 2  h= 1.009e-06
 3  h= 7.566e-07
 4  h= 5.675e-07
 5  h= 4.256e-07
 6  h= 3.192e-07
 7  h= 2.394e-07
 8  h= 1.795e-07
 9  h= 1.347e-07
 10  h= 1.010e-07
 11  h= 7.575e-08
 12  h= 5.681e-08
 13  h= 4.261e-08
 14  h= 3.196e-08
 15  h= 2.397e-08
 16  h= 1.797e-08
 17  h= 1.348e-08
 18  h= 1.011e-08
 19  h= 7.583e-09
 20  h= 5.687e-09
 21  h= 4.266e-09
 22  h= 3.199e-09
 23  h= 2.399e-09
 24  h= 1.800e-09
 h= 1.800e-09
  dfdxb = 1

 Iteration (dx): initial h = 1.795e-06
 1  h= 1.346e-06
 2  h= 1.010e-06
 3  h= 7.574e-07
 4  h= 5.680e-07
 5  h= 4.260e-07
 6  h= 3.195e-07
 7  h= 2.396e-07
 8  h= 1.797e-07
 9  h= 1.348e-07
 10  h= 1.011e-07
 11  h= 7.582e-08
 12  h= 5.687e-08
 13  h= 4.265e-08
 14  h= 3.199e-08
 15  h= 2.399e-08
 16  h= 1.799e-08
 17  h= 1.349e-08
 18  h= 1.012e-08
 19  h= 7.591e-09
 20  h= 5.693e-09
 21  h= 4.270e-09
 22  h= 3.202e-09
 23  h= 2.402e-09
 24  h= 1.801e-09
 25  h= 1.351e-09
 26  h= 1.013e-09
 27  h= 7.599e-10
 28  h= 5.699e-10
 29  h= 4.275e-10
 30  h= 3.206e-10
 31  h= 2.404e-10
 32  h= 1.803e-10
 33  h= 1.353e-10
 h= 1.353e-10
  dfdxb = .99999684

 -----Iteration (dx) for  d^2f/d(xb_k)d(xb_l)-----
 1 
 Iteration (dx): initial h = 1.796e-06
 1  h= 1.347e-06
 2  h= 1.010e-06
 3  h= 7.577e-07
 4  h= 5.683e-07
 5  h= 4.262e-07
 6  h= 3.197e-07
 7  h= 2.398e-07
 8  h= 1.798e-07
 9  h= 1.349e-07
 10  h= 1.011e-07
 11  h= 7.586e-08
 12  h= 5.689e-08
 13  h= 4.267e-08
 14  h= 3.200e-08
 15  h= 2.400e-08
 16  h= 1.800e-08
 17  h= 1.350e-08
 18  h= 1.013e-08
 19  h= 7.594e-09
 20  h= 5.696e-09
 21  h= 4.272e-09
 22  h= 3.204e-09
 23  h= 2.403e-09
 24  h= 1.802e-09
 25  h= 1.352e-09
 26  h= 1.014e-09
 27  h= 7.603e-10
 28  h= 5.702e-10
 h= 5.702e-10
  dfdxb = .99999988
 2 
 Iteration (dx): initial h = 1.797e-06
 1  h= 1.348e-06
 2  h= 1.011e-06
 3  h= 7.583e-07
 4  h= 5.687e-07
 5  h= 4.265e-07
 6  h= 3.199e-07
 7  h= 2.399e-07
 8  h= 1.799e-07
 9  h= 1.350e-07
 10  h= 1.012e-07
 11  h= 7.592e-08
 12  h= 5.694e-08
 13  h= 4.270e-08
 14  h= 3.203e-08
 15  h= 2.402e-08
 16  h= 1.802e-08
 17  h= 1.351e-08
 18  h= 1.013e-08
 19  h= 7.600e-09
 20  h= 5.700e-09
 21  h= 4.275e-09
 22  h= 3.206e-09
 23  h= 2.405e-09
 24  h= 1.804e-09
 h= 1.804e-09
  dfdxb = .99999991
 3 
 Iteration (dx): initial h = 1.799e-06
 1  h= 1.350e-06
 2  h= 1.012e-06
 3  h= 7.592e-07
 4  h= 5.694e-07
 5  h= 4.270e-07
 6  h= 3.203e-07
 7  h= 2.402e-07
 8  h= 1.802e-07
 9  h= 1.351e-07
 10  h= 1.013e-07
 11  h= 7.600e-08
 12  h= 5.700e-08
 13  h= 4.275e-08
 14  h= 3.206e-08
 15  h= 2.405e-08
 16  h= 1.804e-08
 17  h= 1.353e-08
 18  h= 1.014e-08
 19  h= 7.609e-09
 20  h= 5.707e-09
 21  h= 4.280e-09
 22  h= 3.210e-09
 h= 3.210e-09
  dfdxb = 1
 4 
 Iteration (dx): initial h = 1.803e-06
 1  h= 1.352e-06
 2  h= 1.014e-06
 3  h= 7.604e-07
 4  h= 5.703e-07
 5  h= 4.277e-07
 6  h= 3.208e-07
 7  h= 2.406e-07
 8  h= 1.805e-07
 9  h= 1.353e-07
 10  h= 1.015e-07
 11  h= 7.613e-08
 12  h= 5.710e-08
 13  h= 4.282e-08
 14  h= 3.212e-08
 15  h= 2.409e-08
 16  h= 1.807e-08
 17  h= 1.355e-08
 18  h= 1.016e-08
 19  h= 7.622e-09
 20  h= 5.716e-09
 h= 5.716e-09
  dfdxb = 1
 5 
 Iteration (dx): initial h = 1.807e-06
 1  h= 1.355e-06
 2  h= 1.016e-06
 3  h= 7.624e-07
 4  h= 5.718e-07
 5  h= 4.288e-07
 6  h= 3.216e-07
 7  h= 2.412e-07
 8  h= 1.809e-07
 9  h= 1.357e-07
 10  h= 1.018e-07
 11  h= 7.632e-08
 12  h= 5.724e-08
 13  h= 4.293e-08
 14  h= 3.220e-08
 15  h= 2.415e-08
 16  h= 1.811e-08
 17  h= 1.358e-08
 18  h= 1.019e-08
 h= 1.019e-08
  dfdxb = 1
 6 
 Iteration (dx): initial h = 1.814e-06
 1  h= 1.360e-06
 2  h= 1.020e-06
 3  h= 7.652e-07
 4  h= 5.739e-07
 5  h= 4.304e-07
 6  h= 3.228e-07
 7  h= 2.421e-07
 8  h= 1.816e-07
 9  h= 1.362e-07
 10  h= 1.021e-07
 11  h= 7.661e-08
 12  h= 5.746e-08
 13  h= 4.309e-08
 14  h= 3.232e-08
 15  h= 2.424e-08
 16  h= 1.818e-08
 h= 1.818e-08
  dfdxb = 1
 7 
 Iteration (dx): initial h = 1.824e-06
 1  h= 1.368e-06
 2  h= 1.026e-06
 3  h= 7.695e-07
 4  h= 5.772e-07
 5  h= 4.329e-07
 6  h= 3.246e-07
 7  h= 2.435e-07
 8  h= 1.826e-07
 9  h= 1.370e-07
 10  h= 1.027e-07
 11  h= 7.704e-08
 12  h= 5.778e-08
 13  h= 4.334e-08
 14  h= 3.250e-08
 15  h= 2.438e-08
 h= 2.438e-08
  dfdxb = .99999998
 8 
 Iteration (dx): initial h = 1.839e-06
 1  h= 1.380e-06
 2  h= 1.035e-06
 3  h= 7.760e-07
 4  h= 5.820e-07
 5  h= 4.365e-07
 6  h= 3.274e-07
 7  h= 2.455e-07
 8  h= 1.841e-07
 9  h= 1.381e-07
 10  h= 1.036e-07
 11  h= 7.769e-08
 12  h= 5.827e-08
 13  h= 4.370e-08
 h= 4.370e-08
  dfdxb = 1
 9 
 Iteration (dx): initial h = 1.862e-06
 1  h= 1.397e-06
 2  h= 1.048e-06
 3  h= 7.857e-07
 4  h= 5.893e-07
 5  h= 4.420e-07
 6  h= 3.315e-07
 7  h= 2.486e-07
 8  h= 1.865e-07
 9  h= 1.398e-07
 10  h= 1.049e-07
 11  h= 7.866e-08
 12  h= 5.899e-08
 h= 5.899e-08
  dfdxb = 1
 10 
 Iteration (dx): initial h = 1.897e-06
 1  h= 1.423e-06
 2  h= 1.067e-06
 3  h= 8.003e-07
 4  h= 6.002e-07
 5  h= 4.501e-07
 6  h= 3.376e-07
 7  h= 2.532e-07
 8  h= 1.899e-07
 9  h= 1.424e-07
 10  h= 1.068e-07
 11  h= 8.012e-08
 h= 8.012e-08
  dfdxb = 1
 11 
 Iteration (dx): initial h = 1.949e-06
 1  h= 1.461e-06
 2  h= 1.096e-06
 3  h= 8.221e-07
 4  h= 6.166e-07
 5  h= 4.624e-07
 6  h= 3.468e-07
 7  h= 2.601e-07
 8  h= 1.951e-07
 9  h= 1.463e-07
 h= 1.463e-07
  dfdxb = 1
 12 
 Iteration (dx): initial h = 2.026e-06
 1  h= 1.520e-06
 2  h= 1.140e-06
 3  h= 8.548e-07
 4  h= 6.411e-07
 5  h= 4.808e-07
 6  h= 3.606e-07
 7  h= 2.705e-07
 8  h= 2.029e-07
 h= 2.029e-07
  dfdxb = 1
 13 
 Iteration (dx): initial h = 2.143e-06
 1  h= 1.607e-06
 2  h= 1.205e-06
 3  h= 9.039e-07
 4  h= 6.779e-07
 5  h= 5.085e-07
 6  h= 3.813e-07
 7  h= 2.860e-07
 h= 2.860e-07
  dfdxb = 1
 14 
 Iteration (dx): initial h = 2.317e-06
 1  h= 1.738e-06
 2  h= 1.303e-06
 3  h= 9.776e-07
 4  h= 7.332e-07
 5  h= 5.499e-07
 6  h= 4.124e-07
 h= 4.124e-07
  dfdxb = 1
 15 
 Iteration (dx): initial h = 2.579e-06
 1  h= 1.934e-06
 2  h= 1.451e-06
 3  h= 1.088e-06
 4  h= 8.161e-07
 5  h= 6.121e-07
 h= 6.121e-07
  dfdxb = 1
 16 
 Iteration (dx): initial h = 2.972e-06
 1  h= 2.229e-06
 2  h= 1.672e-06
 3  h= 1.254e-06
 4  h= 9.404e-07
 h= 9.404e-07
  dfdxb = 1
 17 
 Iteration (dx): initial h = 3.561e-06
 1  h= 2.671e-06
 2  h= 2.003e-06
 3  h= 1.502e-06
 h= 1.502e-06
  dfdxb = 1
 18 
 Iteration (dx): initial h = 4.445e-06
 1  h= 3.334e-06
 2  h= 2.501e-06
 h= 2.501e-06
  dfdxb = 1
 19 
 Iteration (dx): initial h = 5.771e-06
 1  h= 4.329e-06
 2  h= 3.246e-06
 h= 3.246e-06
  dfdxb = 1
 20 
 Iteration (dx): initial h = 7.760e-06
 1  h= 5.820e-06
 h= 5.820e-06
  dfdxb = 1
 21 
 Iteration (dx): initial h = .00001074
 1  h= 8.058e-06
 h= 8.058e-06
  dfdxb = 1
 22 
 Iteration (dx): initial h = .00001522
 1  h= .00001141
 h= .00001141
  dfdxb = 1
 23 
 Iteration (dx): initial h = .00002193
 1  h= .00001645
 h= .00001645
  dfdxb = 1
 24 
 Iteration (dx): initial h = .000032
 1  h= .000024
 h= .000024
  dfdxb = 1
 25 
 Iteration (dx): initial h = .0000471
 1  h= .00003533
 h= .00003533
  dfdxb = 1
 26 
 Iteration (dx): initial h = .00006976
 1  h= .00005232
 h= .00005232
  dfdxb = 1
 27 
 Iteration (dx): initial h = .00010374
 1  h= .00007781
 h= .00007781
  dfdxb = 1
 28 
 Iteration (dx): initial h = .00015472
 1  h= .00011604
 h= .00011604
  dfdxb = 1
 29 
 Iteration (dx): initial h = .00023118
 1  h= .00017339
 h= .00017339
  dfdxb = 1
 30 
 Iteration (dx): initial h = .00034588
 1  h= .00025941
 h= .00025941
  dfdxb = 1
 31 
 Iteration (dx): initial h = .00051792
 1  h= .00038844
 h= .00038844
  dfdxb = 1
 32 
 Iteration (dx): initial h = .00077598
 1  h= .00058198
 h= .00058198
  dfdxb = 1
 33 
 Iteration (dx): initial h = .00116307
 1  h= .0008723
 h= .0008723
  dfdxb = 1
 34 
 Iteration (dx): initial h = .00174371
 1  h= .00130778
 h= .00130778
  dfdxb = 1
 35 
 Iteration (dx): initial h = .00261467
 1  h= .001961
 h= .001961
  dfdxb = 1
 36 
 Iteration (dx): initial h = .00392111
 1  h= .00294083
 h= .00294083
  dfdxb = 1
 37 
 Iteration (dx): initial h = .00588077
 1  h= .00441058
 h= .00441058
  dfdxb = 1
 38 
 Iteration (dx): initial h = .00882026
 1  h= .0066152
 h= .0066152
  dfdxb = 1
 39 
 Iteration (dx): initial h = .0132295
 1  h= .00992212
 h= .00992212
  dfdxb = 1
 40 
 Iteration (dx): initial h = .01984335
 1  h= .01488251
 h= .01488251
  dfdxb = 1
 41 
 Iteration (dx): initial h = .02976412
 1  h= .02232309
 h= .02232309
  dfdxb = 1
 42 
 Iteration (dx): initial h = .04464529
 1  h= .03348397
 h= .03348397
  dfdxb = 1
 43 
 Iteration (dx): initial h = .06696704
 1  h= .05022528
 h= .05022528
  dfdxb = 1
 44 
 Iteration (dx): initial h = .10044966
 1  h= .07533724
 h= .07533724
  dfdxb = 1
 45 k= 1, l= 1: d^2f/d(xb_k)d(xb_l) = 0
 
 ldose ... continuous
  1   d^2f/dxdb = 1
  2   d^2f/dxdb = 0
 ldose: Std. Err. = 1.7930887
 
 Marginal effects after glm
       y  = linear predictor (predict, xb)
          = -.04312548
 ------------------------------------------------------------------------------
 variable |      dy/dx    Std. Err.     z    P>|z|  [    95% C.I.   ]      X
 ---------+--------------------------------------------------------------------
    ldose |   22.04118     1.79309   12.29   0.000   18.5268  25.5556   1.79343
 ------------------------------------------------------------------------------

The answer is accurate enough, but it sure took some effort to reach it. To see where my scale problem may be, I summarize my data and notice the response variable r has a large range compared with the other variables. So I decide to rescale r and see if that helps:

 . summarize

     Variable |       Obs        Mean    Std. Dev.       Min        Max
 -------------+--------------------------------------------------------
        ldose |         8    1.793425    .0674563     1.6907     1.8839
            n |         8      60.125    2.232071         56         63
            r |         8      36.375    22.55747          6         61
    
 . replace r=r/10
 (8 real changes made)
     
 . glm r ldose, family(binomial n) link(clog)  
 note: r has noninteger values

 Iteration 0:   log likelihood = -12.210073  
 Iteration 1:   log likelihood = -12.202629  
 Iteration 2:   log likelihood = -12.202628  
 
 Generalized linear models                          No. of obs      =         8
 Optimization     : ML                              Residual df     =         6
                                                    Scale parameter =         1
 Deviance         =  1.261310742                    (1/df) Deviance =  .2102185
 Pearson          =  1.264872999                    (1/df) Pearson  =  .2108122
 
 Variance function: V(u) = u*(1-u/n)                [Binomial]
 Link function    : g(u) = ln(-ln(1-u/n))           [Complementary log-log]
 
                                                    AIC             =  3.550657
 Log likelihood   = -12.20262839                    BIC             = -11.21534
 
 ------------------------------------------------------------------------------
              |                 OIM
            r |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
 -------------+----------------------------------------------------------------
        ldose |   10.26508    3.45761     2.97   0.003     3.488291    17.04187
        _cons |  -21.37225   6.326251    -3.38   0.001    -33.77147   -8.973022
 ------------------------------------------------------------------------------
       
 .  mfx, predict(xb)  trace(4) 

 calculating dydx (linear method)

 equation i= 1 
 Iteration (dx): initial h = 1.793e-06
 1  h= 1.345e-06
 2  h= 1.009e-06
 3  h= 7.566e-07
 4  h= 5.675e-07
 5  h= 4.256e-07
 6  h= 3.192e-07
 7  h= 2.394e-07
 h= 2.394e-07
 : df/d(xb) = 1
 
 -------------------------
 variable |      dy/dx
 ---------+---------------
    ldose |       10.265
 -------------------------
 
  
 calculating standard errors (linear method)
  
 equation k = 1: 
 
 Iteration (dx): initial h = 1.793e-06
 1  h= 1.345e-06
 2  h= 1.009e-06
 3  h= 7.566e-07
 4  h= 5.675e-07
 5  h= 4.256e-07
 6  h= 3.192e-07
 7  h= 2.394e-07
 h= 2.394e-07
  dfdxb = 1
 
 Iteration (dx): initial h = 1.795e-06
 1  h= 1.346e-06
 2  h= 1.010e-06
 3  h= 7.574e-07
 4  h= 5.680e-07
 5  h= 4.260e-07
 6  h= 3.195e-07
 7  h= 2.396e-07
 h= 2.396e-07
  dfdxb = 1
 k= 1, l= 1: d^2f/d(xb_k)d(xb_l) = 0
  
 ldose ... continuous
  1   d^2f/dxdb = 1
  2   d^2f/dxdb = 0
 ldose: Std. Err. = 3.4576096
 
 Marginal effects after glm
       y  = linear predictor (predict, xb)
          =  -2.962593
 ------------------------------------------------------------------------------
 variable |      dy/dx    Std. Err.     z    P>|z|  [    95% C.I.   ]      X
 ---------+--------------------------------------------------------------------
    ldose |   10.26508     3.45761    2.97   0.003   3.48829  17.0419   1.79343
 ------------------------------------------------------------------------------
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