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I'm new to both poisson and negative binomial regression models, and am trying to predict a monthly count based on a panel dataset in Stata. I've already set my id and time variables using xtset, and now want to compare the predictions of a poisson and a negative binomial regression model. The general procedure goes as follows:

 xtpoisson y x controlvars, fe irr
 margins, at(time=(1(1)100)) predict(nu0)
 marginsplot

 xtnbreg y x controlvars, fe irr
 margins, at(time=(1(1)100)) predict(nu0)
 marginsplot

From my understanding of the manual, the predict(nu0)-option should calculate the expected number of events at each time interval. Since my data has a lot of overdispersion, I would expect the negative binomial model to provide more accuracte estimates based on my reading of Cameron & Trivedi's brief introduction on the matter (p. 641-642). The regression tables look right based on previous linear modelling attempts, with the negative binomial model having more realistic-looking standard errors as expected. So far so good.

My problem seems to arise when plotting the expected number of events over time. The poisson-regression plots fine and shows the expected trends with an average number of events per time unit of approximately 5 or 6. The negative binomial model, on the other hand, seems to plot an unexpectedly low amount of events per time unit with hardly any development over time (despite regression estimates indicating otherwise). I'm inclined to believe, I may have plotted the model wrongly or missed a transformation option in my coding procedure above. While the poisson-model reports estimates of 5-6 events (as expected), the negative binomial model hovers around 1 event per period with an unexpectedly (based on the incidence rate ratios) slow increase over time.

Is the plotting procedure somehow different for negative binomial models or should I be doing some kind of transformation (ie exponentiation)? It looks like the negative binomial model plots something other than the expected number of events. Or should I simply believe these estimates?

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    $\begingroup$ Note that the results are plotted assuming that the random effects are zero (see help files). Also, the 'fixed effect' NB model does not control for fixed effects in the same way the FE Poisson model does, see eg here and here. I think you're plotting correctly, but I'm not sure how useful it is to compare expected counts for these two models. $\endgroup$ – Matthijs Oct 16 '15 at 9:52
  • $\begingroup$ Thanks for chiming in! I guess I don't really understand why the expected counts for the two models can't meaningfully be compared. How do I interpret the expected counts in the case of the negative binomial plot? I'll make sure to look into the references you posted. Could you find another source (or just post the title) for the last article; for some reason I can't access the link. $\endgroup$ – ageil Oct 16 '15 at 15:22
  • $\begingroup$ The expected counts can be interpreted as in the pooled models, but the individual effects are set to zero. You can check the links on Google Scholar. $\endgroup$ – Matthijs Oct 16 '15 at 18:03

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