# Why does Poisson GLM fit better to non-integer data?

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.

• When you say "best one", in what sense was it best, exactly? – Glen_b May 7 '14 at 2:22
• Prediction error – Evgenii Nikitin May 7 '14 at 11:08
• mean square prediction error? something else? – Glen_b May 7 '14 at 12:40
• MAE, RMSE, cross-validated MAE – Evgenii Nikitin May 7 '14 at 18:56

Take a look at the references in this answer for why a robust poisson model can be applied to non-integer data.

You can also motive it in your case by saying you're modeling a rate per covariate duplicate, as in this question with time. On the other hand, I don't really see a need to aggregate. The Poisson model gives you the expected value conditional on covariates, so it's OK to have duplicates with different outcomes but same covariates.

• First of all, thanks for the references, I'll take a look at them right now. Then, about why I need to aggregate. If I try to predict every observation outcome separately, obviously the average error is higher, there are some effects for duplicates that I don't consider in my model. Since I don't need predictions for every outcome, I don't want to report higher errors. Probably, I'm wrong here, so, please, correct me in this case. – Evgenii Nikitin May 6 '14 at 20:25
• Indeed, I'm modeling a rate per duplicate, but I can't find anything about that in quoted question. Isn't it about an exposure variable? – Evgenii Nikitin May 6 '14 at 20:49
• Your outcome is the total number for a set of duplicates. The exposure variable is the number of duplicates. – Dimitriy V. Masterov May 6 '14 at 21:03