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I'm working with a negative binomial multiple regression and I'm wondering about the assumption of spatial independence of samples. White and Bennetts (1996) say that the assumption of spatial independence is relaxed in negative binomial, unlike Poisson.

Here's the quote from the White and Bennetts 1996 paper on likelihood ratio testing framework for GLMs, which is cited in the text Experimental Design and Data Analysis for Biologists by Quinn and Keough.

The Poisson distribution assumes spatial independence, whereas this assumption is relaxed with the negative binomial distribution.

However, I'm haven't seen this anywhere else and other sources say sample independence is assumed. Can anyone provide any clarification on that?

  • White, G. C., & Bennetts, R. E. (1996). Analysis of frequency count data using the negative binomial distribution. Ecology, 2549-2557.
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That sound like a very strange claim, and it must be meant in some very specific context, which you did not tell us. We really need to know that context ...

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  • $\begingroup$ it probably means that observation were aggregated spatially, since negative binomial deals with autocorrelated events, unlike Poisson $\endgroup$ – carlo Sep 6 '20 at 14:44

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