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It is relatively simple to write the log-density of the negative binomial distribution in terms of its mean, and then use this to get a log-likelihood expression for the negative binomial GLM. For all values $y=0,1,2,...$ the log-density of the negative binomial distribution is: $$\log f(y|r,\theta) = \log {y+r-1 \choose y} + r \log (1-\theta) + y \log (\...


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The answer is: NO, negative binomial regression is NOT CONCAVE when estimated with dispersion. I do not know how to show this mathematically (since negative binomial WITH dispersion parameter does not belong to the exponential family), but I simply found a line in my parameter space, which is not concave. Here it is: Target is the log-likelihood of the ...


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I don't understand what is intended with the phrase "information content". That being said, you might investigate any one of several pseudo r-square measures. Efron's pseudo r-square relies on the difference between the y values predicted by the model and the observed y values. So, it's pretty easy to explain. Some other pseudo r-square values compare ...


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1(a) Anova() can be easier to understand in terms of evaluating the significance of a predictor in your model, even though there is nothing wrong with the output from summary(). The usual R summary() function reports something that can appear quite different from Anova(). A summary() function typically reports whether the estimated value for each ...


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