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To the best of my knowledge, the dependent variable (outcome) in a negative binomial regression should ideally represent count data. In R, if the interest is to model rates, I understand the use of +offset(log(population)) in glm.nb or glmmadb .

My question is related to conditions for other covariates. Are incidence/prevalence rates appropriate for additional independent variables? For example, if I'm trying to control for the incidence rate of diabetes per 100,000 within a group, could that be an acceptable independent variable in the negative binomial model?

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  • $\begingroup$ as long as it has a linear relationship with your dependent variable it should be ok. Also remember to center it $\endgroup$
    – StupidWolf
    May 15, 2020 at 22:10
  • $\begingroup$ Thanks for the response. What do you mean by centering? $\endgroup$ May 15, 2020 at 23:50
  • $\begingroup$ you minus the mean of the variable off.. that is you center the variable around its mean. check the answer by macro from stats.stackexchange.com/questions/29781/… $\endgroup$
    – StupidWolf
    May 15, 2020 at 23:55
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    $\begingroup$ @stupidwolf with negative binomial regression the relationship with the dependent variable would depend on the link function being used $\endgroup$
    – Glen_b
    May 16, 2020 at 11:17
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    $\begingroup$ @Glen_b-ReinstateMonica, thanks for pointing that out. SahitMenon, by default glm.nb in R fits it with a log link, so you should check that the log of the rates shows a linear relationship with your condition / covariates $\endgroup$
    – StupidWolf
    May 17, 2020 at 10:46

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