Let's assume that I have a set of predictors and a non-negative integer resulting variable (number of events). All observations are repeated few times (it means that all predictors have the same values more than once). I need to predict an average number of events for every possible combination of predictor's values. I combined all observations with the same predictors' values to one, and assigned an average number of events for all these observations to the new one.
Next, I built four different models - OLS, OLS with transformed resulting variable, hurdle Gamma GLM and, I don't know why, Poisson GLM. Surprisingly, Poisson was the best one. Since this is my final qualification thesis, I need some theoretical basis, but I can't figure one, I've been always thinking that Poisson regression assumes integer data. Hope, somebody could help.