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I will try to keep this short.

As an assignment for my GLM course, we were given a dataset on the # of homicide victims a person knows, as well as the race of the person. The main idea is to answer the scientific question "Does race help explain how many homicide victims a person knows?". This same dataset, and actually nearly all the sub-problems are solved here: https://data.library.virginia.edu/getting-started-with-negative-binomial-regression-modeling/.

My issue is, I am struggling to understand the difference between the 3 models. My understanding is that the model is a tool that I use to help me predict something. In this example, the race is meant to help me predict the # of homicides someone knows. Therefore, if all 3 models give me identical coefficients, then my predictions will all be identical. This leads me to be very confused, as the models are said to not be identical, and have different residuals, etc...

I don't understand how this is possible, and don't understand what I could be missing. It seems like it should be very simple as the prediction is being made using only 1 binary variable, and so there are only 2 options for each prediction, and the identical coefficients should create identical predictions...

Thanks a lot for any help in advance.

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  • $\begingroup$ in the tutorial it is mentioned that Poisson dist assumes same mean and variance. While Negative Binomial dist has a dispersion coeff that makes variance different than the mean. So for the race example the Poisson modelling exhibits variance same as the mean, while it is mentioned that this is not so from the data analysis $\endgroup$
    – Nikos M.
    Commented Mar 20, 2021 at 19:21
  • $\begingroup$ The coefficients you mention even though they might be the same for this case, they are used in different models. Hence the different results (eg in std. error) $\endgroup$
    – Nikos M.
    Commented Mar 20, 2021 at 19:26

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