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  • Is there a command for rare events *probit* estimation?

    Hi all
    I know there are few methods to estimate a logistic regression when the binary dependant variable has rare events (very few ones relative to many zeros).
    In a draft of my paper, I showed results using a standard probit model. I was then advised by the reviewer to show robustness of my results after considering the fact that the event is very rare.

    The problem is that I prefer to be consistent and use a probit model rather than a loigit model but as far as I can see the only available ones are those of logit such as
    Code:
    firthlogit or relogit
    .

    Does anyone have more information regarding this?

    Thanks

  • #2
    If you can't find a program you may just wish to say that one doesn't exist so you used logit instead.

    You may also wish to look at http://statisticalhorizons.com/logis...or-rare-events. Rare events aren't necessarily a problem if you have a very large data set.
    -------------------------------------------
    Richard Williams, Notre Dame Dept of Sociology
    Stata Version: 15.1MP (2 processor)

    EMAIL: rwilliam@ND.Edu
    WWW: https://www3.nd.edu/~rwilliam

    Comment


    • #3
      Incidentally, I wonder how hard it would be to turn firthlogit into firthprobit, and how appropriate it would be to do so. Perhaps Joseph Coveney could comment.
      -------------------------------------------
      Richard Williams, Notre Dame Dept of Sociology
      Stata Version: 15.1MP (2 processor)

      EMAIL: rwilliam@ND.Edu
      WWW: https://www3.nd.edu/~rwilliam

      Comment


      • #4
        Thanks Richard, I read the post you suggested. I think the events are rare. They are the peaks in the business cycle ( 7 ones relative to 170 zeros).

        It would be ideral if one can develop something like **reprobit** or **firthprobit** !

        Is this possible?

        Comment


        • #5
          Hi all
          I think that shifting from a standard probit in my case to a a " special case" logit is not pleasent, isn't it? Do you think that this can be jusdtified? It will really ideal if there are any programmes that can emply a probit in rare events.

          Look forward to hearing from you, Stata team.

          Thanks
          Lisa

          Comment


          • #6
            Firth's bias reduction can be done for non-canonical link functions. It's not been done in Stata to my knowledge.

            I'm not sure why you cannot assess the robustness of your results by inspection of the coefficients or predictions from -firthlogit-.

            Comment


            • #7
              I agree with Joe that I don't see anything too bad about using the current firthlogit. But, if you really really really want probit, then in the "use at your own risk" category:

              firthlogit_ll.ado includes these two lines:

              generate double `mu' = invlogit( `xb') if $ML_y1 == 1
              replace `mu' = invlogit(-`xb') if $ML_y1 == 0


              I changed them to

              generate double `mu' = normal( `xb') if $ML_y1 == 1
              replace `mu' = normal(-`xb') if $ML_y1 == 0

              As far as I can tell, that changed the link function from logit to probit. (I ran both probit and revised firthlogit on a larger sample and results were almost identical).

              Perhaps Joseph Coveney can comment on whether he thinks this is a terrible mistake, e.g. is there something else that also needs to be changed?
              -------------------------------------------
              Richard Williams, Notre Dame Dept of Sociology
              Stata Version: 15.1MP (2 processor)

              EMAIL: rwilliam@ND.Edu
              WWW: https://www3.nd.edu/~rwilliam

              Comment


              • #8
                That sounds interesting Richard.
                Joseph , can you please share your views on that?

                Thanks
                Lisa

                Comment


                • #9
                  Yes: don't do it.

                  Rather: examine the model fitted by -firthlogit- or the other one, -reprobit-, or yet another one, -penlogit- (use Stata's -search- command to find from where to install it) and assess whether the results you got with -probit- are sufficiently robust, and then speak to the referee's comment.

                  Comment


                  • #10
                    It is a good thing we asked Joe! Is it more complicated than what I did, or is probit just not appropriate in the first place?

                    In any event, I would go with the established programs rather than take a chance with my ad hoc improvisation if there is doubt as to its correctness.
                    -------------------------------------------
                    Richard Williams, Notre Dame Dept of Sociology
                    Stata Version: 15.1MP (2 processor)

                    EMAIL: rwilliam@ND.Edu
                    WWW: https://www3.nd.edu/~rwilliam

                    Comment


                    • #11
                      Hi Lisa,

                      This is a bit of a tangent, but I'd be tempted to run -firthlogit- and -exlogistic- and/or something Bayesian [Stata directly, or Gelman's weakly informative prior in R (via -Rsource- or -Rcall-, both from SSC) and if your conclusions are unchanged, then I'd just highlight the consistency to the reviewer and move on. Trying to troubleshoot/test/validate something potentially novel like firthprobit is maybe unreasonable!
                      Last edited by Andrew Lover; 30 Mar 2017, 07:10.
                      __________________________________________________ __
                      Assistant Professor, Department of Biostatistics and Epidemiology
                      School of Public Health and Health Sciences
                      University of Massachusetts- Amherst

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