I have aggregated death counts and some categorical predictors e.g. era, drug use, and I'm running a Poisson GZLM in SPSS, also a glm in Stata (generalized linear model). There are many, but not excessive, zeros and it has been suggested to me to add 0.5 to the observed values. When I do that the GENLIN procedure in SPSS won't run, because the Poisson dependent should have integer values. However, the glm with family Poisson and log link in Stata runs and just makes a note that the dependent has non-integer values. Why does Stata run the Poisson glm if the values of the dependent should be integers only?

Thank you all