I have a simple poisson glm with one predictor that has three levels. Unfortunately, for one level my response, the variable has only counts of zero. I expected very low counts (perhaps a one or a two at most). Because of one level having all zeros, neither my poisson glm, nor "zeroinfl" (from pscl), work. The glm throws out a massive standard error for the all zero factor level and the zeroinfl gives me an error message.
Is there a statistical way to say that the other two groups are different from the one with all zeros?