Further, how can a duration be binomially distributed? Unless you are defining an incidence as a duration, such as behavior not seen --> duration=0, behavior seen -> 1.   But your issue is with the first analysis, and the problem is that the log of 0 is negative infinity, so folks say you can't analyze the results when you have a zero and a log link. There are alternatives, and you are part way there by picking a multiplicative overdispersion. Consider adding a small (say 1e-6) to every observation, and fitting a gamma distribution (although you can still fit a Poisson, let's just move to the continuous version rather than staying with the discrete version). That should address your model. It is harder to compare means except on the log scale. The ILINK option gives a ratio for the exponentiated difference of two means on the log scale, not the difference on the measured scale of two exponentiated estimates. I don't know if the %NLest macro would be appropriate here, but it certainly is appropriate for the Poisson distribution example. Perhaps @StatDave could chime in here on that approach.   SteveDenham ... View more