How to measure goodness of fit for a poisson regression model? I am working on a poisson regression model in sas. But I am not able to determine how good the fit is. I have used PROC GENMOD, PROC NLMIXED, PROC GLIMMIX and now I want to compare the results. How can I do that?
Is there any other way to do a poisson regression in sas?
P.S. I have tried both Poisson and Negetive Binomial Distributions.
 A: From the little I know about SAS, you want to compare a GLM (Generalised Linear Model - PROC GENMOD), a GLMM (Generalized Linear Mixed Model - PROC GLIMMIX) and a Nonlinear Mixed Model (NLMM - PROC NLMIXED) all with poisson (or negative binomial) outcomes. With the same outcome and the same predictors, a GLMM and NLMM should give the same results provided that the same distribution, link function and estimation method are used, so the question comes down to comparing the fits of a GLM and a GLMM. 
Usually, the question of whether to use a GLM or a GLMM can be answered by considering the data and how it arose. If the data are independent then a GLM is warranted, subject to the usual assumptions, but if there is clustering of data, for example due to repeated measures or a natural cross-sectional data hierarchy such as pupils in schools, or animals in farms, then a GLMM is more appropriate, where random effects are introduced into the model to account for observations in one cluster being more similar to observations in the same cluster than other clusters.  So if you have clustering, it is better to fit a GLMM than a GLM. In order to compare model fit statistically, if the two models have the same fixed effects then a likelihood ratio test can be used. 
Since poisson regression is a special case of negative binomial, you can also use a likelihood ratio test to compare the fit of these.
Another approach worth mentioning is to compare the predictions of the models, and choose the model with the best prediction capability. This works especially well if you use cross-validation.
