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What relationship does a negative binomial regression have to heteroskedasticity and if one still needs to check and/or correct for it how would this be done?

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  • $\begingroup$ Negative binomial models are often suggested for count data, when the data doesn't look Poisson. But if you just want to do regression without specifying a particular mean-variance relationship, and have at least a moderate sample size, apply robust standard errors to e.g. Poisson regression output. Also, is this a homework question? $\endgroup$ – guest Mar 20 '12 at 7:01
  • $\begingroup$ No. A project question. I have real count data and DP which I want to put into a NB. I've tested for multicollinearity and over dispersion, but as NB partly accounts for heteroskedasticity I was wondering what other tests I should consider applying to the data after. $\endgroup$ – Stephen Mar 20 '12 at 15:03
  • $\begingroup$ You could try plotting the absolute value of Pearson residuals from your NB regression against covariates (at least, covariates you think might affect the overdispersion) or against the fitted means. If there's a discernible trend, this suggests non-constant variance. Alternatively, compare your NB output to what you get under the "robust" approach I mentioned; informally, little difference between the two would suggest little to worry about. $\endgroup$ – guest Mar 20 '12 at 22:58
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Heteroskedasticity is relevant with ordinary linear regression, where there is an assumption that variance is constant (do not depend on the mean), known as homoskedasticity. But with alternative regression models, like poisson regression or negative binomial regression, there is no assumption of constant variance! In its place this models do assume some other mean-variance relationship, in the case of poisson regression that the variance=mean. For negative binomial regression, there o exist several variants with different mean-variance relationships. So in place of investigating violation of homoskedasticity, you should investigate violation of the assumed mean-variance relationship. You could start with a plot of residuals versus predicted values.

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