So now, looking at an individual observation with "Variable" = 0, I'd like to know the odds of that observation producing a zero (without considering the poisson distribution). My understanding is that this probability is
exp(0.525351) * exp(-0.783426) ^ 0
or just exp(0.525351) = 1.69
Obviously 1.69 is not a legitimate probability. What am I missing? By the way, it is fully possible for "Variable" to equal zero in this dataset.
The probability of a zero is not a function of only the zero-inflation parameters. There are two processes at play that each contribute to the probability. The probabilities of various counts (including zero) can be computed by the PROBCOUNTS macro available in this sample program: