Timeline for Rule of thumb for deciding between Poisson and negative binomal models
Current License: CC BY-SA 4.0
3 events
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| Nov 10, 2023 at 22:34 | comment | added | PBulls |
These tests are only for Poisson fits, to check whether mean and variance are indeed the same. In a NB model the variance is a second parameter so they do not apply. I think you can still use the Pearson statistic for NB as you do for Poisson, there are other models (e.g. NB with parametrized exponent, Poisson-inverse-Gaussian) that can handle even more overdispersion but 0.94 seems quite OK. FYI, the data were taken from the glm.nb example so I would assume a NB model is appropriate here. I only just learned about the DHARMa package which may also be useful for goodness of fit.
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| Nov 10, 2023 at 22:22 | comment | added | C. Murtaugh |
Thanks for a detailed explanation and worked example. It does seem like the Pearson dispersion statistic makes the most sense as a simple way to analyze the data. I'm not sure how one would compare the Poisson vs NB models using the score test, however. In the worked model, the t test of poi_glm gives p=4.6e-9. If I use glm.nb to analyze the same data, I get a t test p=2.5e-8. I'm not sure how to compare these. If I run a two-sample t test on the NB vs Poisson z values, I get p=0.90.) Whether meaningful or not, the Pearson statistic of the NB model is 0.94, vs 10.5 for Poisson.
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| Nov 8, 2023 at 9:59 | history | answered | PBulls | CC BY-SA 4.0 |