I am looking at homicide rates per US county in a given 3-yr period as a DV, against several demographic and political measures as IV. I have A LOT of zeros for the DV, and these are presumably real zeros. My research has indicated that if I were using count data instead of rates, this would be a great match for ZIP or ZINB, which are available in R in the package pscl. However, it does not handle continuous data, in this case, homicide rates. The package CPLM has a compound poisson (tweedie) function for zero-inflated data, zcpglm, which assumes a continuous DV. It seems to handle the data well and produces reasonable-looking results (the results are very similar to what I get from ZINB if I round the rates to get integers so I can process them as counts).
Presuming the validity of the above choices, I would like to generate some goodness of fit tests. I can get a log-likelihood from zcpglm, so I can compare models to each other that way. But I would like to calculate deviance, and see if a pseudo-R^2 measure is possible, using
(from Heinzl & Mittlbock, Pseudo R-squared measures for Poisson, 2003).
The problem is that zcpglm does not provide the deviance, and I don't know how to create a saturated model to calculate the LL. The null model seems easy enough.
I have found examples for saturated models for a gaussian, poisson, ZIP & ZINB. But the latter three are only for count data, and this model clearly is neither count, nor gaussian. The p (index parameter) = 1.99 (and phi=0.46), indicating this is a gamma-like compound distribution, and a histogram seems to confirm it. But again, I'm not sure how to create a saturated model for a gamma distribution, and since this is a 2-part model anyway, it's making me even more stuck.