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  • Testing for overdispersion glm negative binomial regression


    I am working with time series count data. I use Newey-West SEs and therefore need to use the glm command to estimate the negative binomial regression. Specifically, the command I use is glm ..., family(nbinom ml) vce(hac nwest 7).

    Just by looking at the distribution of the dependent variable, you can tell that it clearly exhibits overdispersion. This is further supported by the likehood ratio test restricting the overdispersion parameter 𝛼 = 0 that you get from the standard nbreg command.

    However, I cannot seem to find the equivalent test for the negative binomial regression estimated using glm. Any ideas on how to find this?


  • #2
    As a general matter one can't determine overdispersion (presumably with respect to a Poisson distribution?) just by examining the distribution of the dependent variable since in most interpretations overdispersion refers to properties of the conditional distribution not the marginal distribution, i.e. var(y|x)>E(y|x), not var(y)>E(y).

    In glm the family(nbinom ml) option embeds the nbreg ML estimate of alpha and optimizes conditional on it whereas specifying family(nbinom) effectively restricts alpha=1. I'm not sure of a specific test but am wondering if a comparison of the estimates of these two glm specifications based on deviance, AIC, BIC, etc. might provide the basis of such a test. Hopefully others will weigh in on this since this is only a speculation on my part.


    • #3
      Thank you. It was sloppy writing by me. I fully agree with your point about the conditional distribution.

      Yours is a good suggestion. I will have a closer look at the goodness-of-fit statistics for the different models.


      • #4
        as an aside to John's helpful insight, Stata users dealing with -glm- often take (much more than) a look at the wonderful and comprehensive
        Unfortunately for the statistic/Stata community, this valuable textbook represents one of the last collaboration of James W. Hardin with the deeply missed Joe Hilbe.
        Kind regards,
        (Stata 16.0 SE)


        • #5
          Carlo: Thank you very much. I have put in an order at the library for the book and I am sure that it will be very helpful.