Poisson errors with positive non integer data

[deleted_user]

Dear all,
I have constructed a mixed effect model in SAS using the %glimmix macro.
I have count data with many zeros and have found that a square root transformation of my data (sqrt(x+1)) prior to analysis greatly improves the fit of my models (in some cases the models don't run at all without the transformation). As my data are counts I have used a poisson error distribution, which works far better than normal/negbin/gamma errors. I am aware the poisson distribution is normally for non negative integers but the model runs without any problems and I am wondering if it is acceptable to use poisson in this way as I have read in some cases non negative decimals can be ok?
Thanks in advance

[StatDave]

I'm a little unclear on your question since, on the one hand, you say your data are counts implying that they are integers, but on the other hand suggesting that they are not integers. If your data are not nonnegative integers, then they cannot be poisson distributed. However, you can still fit a poisson model using PROC GENMOD. GENMOD will tell you in the log that noninteger values were detected, but it will proceed normally. While the data cannot be poisson, the resulting model may still be useful for some purposes.

As a side note, if you do have integer count data with more zeros that would be expected, you can fit a zero-inflated poisson model. This is available in PROC COUNTREG (in SAS/ETS software) and, beginning in SAS 9.2, in PROC GENMOD. Sometimes a negative binomial model does a better job of accounting for excess zeros, and you can use both procedures to fit that model too. PROC COUNTREG can also fit a zero-inflated negative binomial model.

[mlince]

What would be the way to compare the fit of both negative binomial or zero inflated possion with the poisson regression?