Hello Statalisters,
Can anyone explain why Poisson regression returns the pooled rate across observations, while negative binomial regression returns the mean rate? These can be quite different if the exposure times vary significantly between observations.
See the following example
Results are as shown below
I am using Stata/BE 18.0 on Windows 11
To me at least, the pooled rate seems more intuitive and more robust to extreme values which may arise due to short exposure times. I would be interested in any insights.
This is not peculiar to Stata, I had a friend test it in R with the same result.
C
Can anyone explain why Poisson regression returns the pooled rate across observations, while negative binomial regression returns the mean rate? These can be quite different if the exposure times vary significantly between observations.
See the following example
Code:
webuse rod93, clear drop cohort age gen Rate = deaths/exposure //indivudul rates egen MeanRate = mean(Rate) //mean of the individual rates egen TD = total(deaths) egen TF = total(exposure) gen PooledRate = TD/TF //Pooled rate nbreg deaths, irr exp(exposure) predict nb_rates, ir //rate as predicted by negative binomial model poisson deaths, irr exp(exposure) predict poisson_rates, ir //rate as predicted by poisson model keep MeanRate PooledRate nb_rates poisson_rates duplicates drop dataex
Results are as shown below
Code:
* Example generated by -dataex-. For more info, type help dataex clear input float(MeanRate PooledRate nb_rates poisson_rates) .09991664 .018380756 .099155 .018380757 end
I am using Stata/BE 18.0 on Windows 11
To me at least, the pooled rate seems more intuitive and more robust to extreme values which may arise due to short exposure times. I would be interested in any insights.
This is not peculiar to Stata, I had a friend test it in R with the same result.
C
