Firthlogit postestimation

[Miguel Angelo]

Hello,
I'll need help with the estimation of marginal effects using firthlogit.

I'm working with dummy as dependent variable that has an inflated number of 0 over 1 (almost 90%).
I'm using the firthlogit to implement a penalized maximum likelihood estimation method for reducing bias in the distribution suggested by Coveney (2015).
However when I tried to estimate marginal effects but the results are very weird.

For instance, Odd ratios from estimations in are positive but marginal effect comes all negative.

Thanks

[Clyde Schechter]

Odds ratios are always positive. The "null value" of the odds ratio is 1, not 0. Odds ratios < 1 correspond to negative marginal effects, those > 0 correspond to positive marginal effects.

If your outputs appear to contradict that, then to get more concrete advice, please post back showing the actual output of both -firthlogit- and -margins- along with the commands you used to get those. In doing that, please be sure to place the output between code delimiters so that it is easily readable. If you are not familiar with using code delimiters, you will find them explained in Forum FAQ #12.

[Richard Williams]

Questions like this come up periodically. The results are probably fine, you are just misinterpreting what they are. See especially posts 4 and 5 of

https://www.statalist.org/forums/for...hood-estimates

[Miguel Angelo]

Thank you all for the feed back.
I manage to solve the issue using :

margins Variable, expression(invlogit(predict(xb)))

[Richard Williams]

For more on analyzing rare events, you might want to see

https://www3.nd.edu/~rwilliam/stats3/RareEvents.pdf

[Jason Campos]

Hi Richard. Just a question: why might I want to use the xb over pr after a firthlogit (e.g. firthlogit y x1 x2 x3) regression command? I am in a similar boat as OP and need some feedback. My main issue is that I am not sure if I should be using the regular margins command after firthlogit versus adding the express xb (for predicting if Y=1). My Y is a binary variable, as well as both my independent (main variables). Examples of what I see are the following:

When I type the written command:

 margins, dydx(gangm) expression(invlogit(predict(xb)))

I get this output:

Average marginal effects                        Number of obs     =     23,919
Model VCE    : OIM

Expression   : invlogit(predict(xb))
dy/dx w.r.t. : gangm

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       gangm |   .0362728   .0170578     2.13   0.033       .00284    .0697055
------------------------------------------------------------------------------

When I type the regular, command

 margins, dydx(gangm)

I get this output (below), which is completely separate from when I include the (invlogit(predict(xb)))

Average marginal effects                        Number of obs     =     23,919
Model VCE    : OIM

Expression   : Linear prediction, predict()
dy/dx w.r.t. : 1.gangm

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       gangm |
        YES  |   .1707991   .0803539     2.13   0.034     .0133084    .3282898
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

For context, I have provided a picture of my model. Any feedback is appreciated.

firthlogit report i.gangm intim3 i.vrace i.gender i.landtype i.V2127B

initial:       penalized log likelihood = -15636.338
rescale:       penalized log likelihood = -15636.338
Iteration 0:   penalized log likelihood = -15636.338  
Iteration 1:   penalized log likelihood = -14384.739  
Iteration 2:   penalized log likelihood = -14218.414  
Iteration 3:   penalized log likelihood = -14184.754  
Iteration 4:   penalized log likelihood = -14178.379  
Iteration 5:   penalized log likelihood = -14177.756  
Iteration 6:   penalized log likelihood =  -14177.72  
Iteration 7:   penalized log likelihood =  -14177.72                                                   Number of obs     =     23,919
                                                Wald chi2(13)     =     113.78
Penalized log likelihood =  -14177.72           Prob > chi2       =     0.0000

-------------------------------------------------------------------------------------------------
                         report |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------------------+----------------------------------------------------------------
                          gangm |
                           YES  |   .1707991   .0803539     2.13   0.034     .0133084    .3282898
                         intim3 |  -8.328734   1.414964    -5.89   0.000    -11.10201   -5.555456
                                |
                          vrace |
                         BLACK  |   .1322671   .0438009     3.02   0.003     .0464189    .2181153
             AM/ ALASKA NATIVE  |  -.0211212   .1271436    -0.17   0.868    -.2703181    .2280757
                         ASIAN  |    -.00106   .0968429    -0.01   0.991    -.1908686    .1887486
               HAWAIIAN,
              PACIFIC ISLANDER  |  -.1307301   .2592881    -0.50   0.614    -.6389255    .3774653
                         OTHER  |  -.0839671   .0839718    -1.00   0.317    -.2485487    .0806145
                      HISPANIC  |   .0880073   .0447727     1.97   0.049     .0002543    .1757602
                                |
                         gender |
                        FEMALE  |   .1152622   .0333234     3.46   0.001     .0499496    .1805747
                                |
                       landtype |
                         RURAL  |   .1329574   .0386626     3.44   0.001       .05718    .2087348
                                |
                         V2127B |
                       Midwest  |   .0342033   .0470017     0.73   0.467    -.0579183     .126325
                         South  |   .1370015   .0456354     3.00   0.003     .0475577    .2264453
                          West  |   -.059097   .0473682    -1.25   0.212    -.1519369    .0337429
                                |
                          _cons |  -.5266472   .0473121   -11.13   0.000    -.6193773   -.4339171