Zero Inflated Negative Binomial Model

[FishModeler]

Hello! I am looking for help/resources to guide me on how to change this zero-inflate Poisson model into zero-inflated negative binomial model. I don't see a function like dzipois that would easily take care of this issue. Could I somehow use dgampois in a zero-inflated negative binomial model? Any ideas? Thank you!!!

SitePoisson <- ulam(
alist(
SportfishCount ~ dzipois(pbar,lamba),
logit(pbar) <- z1+z2*Dim2
log(lamba)a + b * Dim1+c * Dim2+d * HTOY,
a ~ dnorm(1.85,2.76),
b ~ dnorm(1,100),
c ~ dnorm(1,100),
d ~ dnorm(0,1),
c(z1,z2)~dnorm(0,1)
),
data = ModelData,
start=list(a=0,b=0,c=0,d=0,z1=0.1,z2=0.2),
iter=5000,warmup=2000,chains =3, cores = 4, log_lik = TRUE
)

[rmcelreath]

There is no template for zigampois unfortunately. I can add it to the feature list. It is just a slight modification of dzipois.

In the meantime, you could get very close to zigampois by just adding random intercepts on each observation. That will add dispersion like a negative-binomial. It might be hard to get it to sample right, unless it is non-centered however.

Another approach is the modify the Stan code, if you are comfortable doing that. You can replace poisson with an appropriately parameterized negative-binomial. That's all that should be necessary.