# Inferences from a zero-inflated negative binomial distribution?

Frogs are generally known to spatially aggregate during egg-laying. I manipulated their egg-laying sites with different fertilizers ("Nitrogen" or "Phosphorous") that differed in their concentration ("Low" or "High"). I wanted to calculate their index of aggregation using zero-inflated negative binomial models. I got the following results. From this output, how can I infer the index of aggregation (as in the variance: mean ratio) for each fertilizer type x level? Is the model coefficients itself the index of aggregation? Do I need to do some-other transformations?

It's hard to say what exactly is going on based on the information provided. But two things are suspicious:

1. The zero inflation model has an intercept which is extremely small and only the fertilizerP x levellow interaction term is reasonably large. This indicates that there is virtually no zero inflation, except possibly for a few of the groups in the experimental design.

2. The log(theta) in the count model is very small, indicating a high overdispersion. This also looks suspicious, not sure what exactly this is caused by.

I would recommend doing some more exploratory analysis, especially visualizations of the four subgroups. For modeling a hurdle() model might be easier to interpret.

• This is just a representative example. I'm trying to generally understand how Fischer's variance to mean ratio relates to the negative binomial model. – Biotechgeek Sep 25 '19 at 20:29