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?