Dear members,

I am running a parametric survival model with a lognormal distribution. My dataset is a firm-year panel. Firms are observed every year from inception until either they experience the event (coded as 1) or the time window of the study ends (coded as 0).

I am interested to estimate average margins effects at the means (MEMs) for my independent variable which is a categorical variable (firm location) assuming 3 potential values (0=urban; 1=suburban; 2=rural) on the dependent one (firm survival). I also have a time-variant control in my model. I obtain the following results from my analysis:

Code:

. streg control1 i.firm_location,vce(robust) d(lognormal) time
 
         failure _d:  failed1 == 1
   analysis time _t:  (year-origin)
             origin:  time cohort
                 id:  FAD_F_Id
 
Fitting constant-only model:
 
Iteration 0:   log pseudolikelihood = -16363.037
Iteration 1:   log pseudolikelihood = -15818.866
Iteration 2:   log pseudolikelihood = -15780.064
Iteration 3:   log pseudolikelihood = -15779.955
Iteration 4:   log pseudolikelihood = -15779.955
 
Fitting full model:
 
Iteration 0:   log pseudolikelihood = -15779.955
Iteration 1:   log pseudolikelihood =  -15711.05
Iteration 2:   log pseudolikelihood = -15710.045
Iteration 3:   log pseudolikelihood = -15710.045
 
Lognormal AFT regression
 
No. of subjects      =       11,773             Number of obs    =      50,000
No. of failures      =        8,559
Time at risk         =        50000
                                                Wald chi2(3)     =      105.31
Log pseudolikelihood =   -15710.045             Prob > chi2      =      0.0000
 
                           (Std. Err. adjusted for 11,773 clusters in FAD_F_Id)
-------------------------------------------------------------------------------
              |               Robust
           _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
     control1 |   .1205071   .0173318     6.95   0.000     .0865374    .1544769
              |
firm_location |
    suburban  |  -.1840696   .0359398    -5.12   0.000    -.2545103   -.1136288
       rural  |   .1961607   .0793339     2.47   0.013     .0406691    .3516523
              |
        _cons |    1.34495    .040215    33.44   0.000      1.26613     1.42377
--------------+----------------------------------------------------------------
     /lnsigma |   .0567524   .0062428     9.09   0.000     .0445167    .0689882
--------------+----------------------------------------------------------------
        sigma |   1.058394   .0066074                      1.045522    1.071424
-------------------------------------------------------------------------------
 
.
. margins firm_location, atmeans
 
Adjusted predictions                            Number of obs     =     50,000
Model VCE    : Robust
 
Expression   : Predicted median _t, predict()
at           : control1        =     1.24962 (mean)
               0.firm_loc~n    =      .10254 (mean)
               1.firm_loc~n    =      .86862 (mean)
               2.firm_loc~n    =      .02884 (mean)
 
-------------------------------------------------------------------------------
              |            Delta-method
              |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
firm_location |
       urban  |   4.461736    .154031    28.97   0.000      4.15984    4.763631
    suburban  |   3.711619   .0426361    87.05   0.000     3.628054    3.795185
       rural  |   5.428694   .3888111    13.96   0.000     4.666638    6.190749
-------------------------------------------------------------------------------
 
.
. margins r.firm_location, atmeans
 
Contrasts of adjusted predictions               Number of obs     =     50,000
Model VCE    : Robust
 
Expression   : Predicted median _t, predict()
at           : control1        =     1.24962 (mean)
               0.firm_loc~n    =      .10254 (mean)
               1.firm_loc~n    =      .86862 (mean)
               2.firm_loc~n    =      .02884 (mean)
 
--------------------------------------------------------
                     |         df        chi2     P>chi2
---------------------+----------------------------------
       firm_location |
(suburban vs urban)  |          1       22.50     0.0000
   (rural vs urban)  |          1        5.37     0.0205
              Joint  |          2       40.78     0.0000
--------------------------------------------------------
 
----------------------------------------------------------------------
                     |            Delta-method
                     |   Contrast   Std. Err.     [95% Conf. Interval]
---------------------+------------------------------------------------
       firm_location |
(suburban vs urban)  |  -.7501162   .1581513     -1.060087   -.4401454
   (rural vs urban)  |    .966958   .4174105      .1488485    1.785068
----------------------------------------------------------------------
The way I would interpret the results from the MEMs analysis is the following:

the median survival time for suburban firms, compared with urban firms, is, on average, 75 percentage points lower. Conversely, the median survival time for rural firms, compared with urban firms, is, on average, 97 percentage points higher.

I would also be interested to provide what I believe to be a more straightforward interpretation using the results from the adjusted predictions. I would do so in the following way:

on average, the median survival time of suburban firms is 17% lower than the one of urban firms. Conversely, the median survival time of rural firms is 22% higher than the one of urban firms.

Would you agree with these interpretations?

Thanks in advance,

Giuseppe