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Negative binomial model - saturated?

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I am trying to run a model for cases (n) to see if area, period, and area*period are significant predictors. I am really only interested in the area*period component because the two variables on their own don't make much sense as I need to compare the cases over time between the 3 areas.

So for some of the instances, I run the model and get zeros for some of the goodness of fit parameters and then get p=1.000 in the LR statistics output. I was told that this is correct for my data and that it means the model is saturated. So when one has a saturated model is there anything to do? I can't really break down the data in any way in this case. Or do you just have to ignore this type of result or what? Sorry, I've never had a scenario like this. Thanks!

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