Beta-binomial N-mix with p-rho parameterization

[Gates Dupont]

Hi all,

I'm interested in using the beta-binomial observation model for an N-mixture model, as described in this linked paper, but I would like to implement the p-rho parameterization rather than the alpha-beta that they implement.

Briefly, here's how they accomplish the BBP N-mix:

# Observation model for replicated counts

for (i in 1:n) {​ # Loops over all n observations

C[i] ~ dbin(p[i], N[site.p[i]]) # counts follow a beta-binomial distribution

       p[i]~dbeta(alpha.p,beta.p)  # detection probability p follows a beta distribution

}

The p-rho would be where p is the probability parameter and rho is a correlation parameter. I would rather use the p-rho because currently I have covariates on p. I think this is the version that the dNmixture_BBP_*() functions use, which is great, but then I'm not sure how to carry out PPC/GOF tests when using the nimbleEcology distributions.

Might anyone be able to pass along example code for the p-rho beta-binomial, or instead example code for a PPC/GOF test using dNmixture_BBP_*()?

Sincere thanks!

Best,

Gates Dupont

[Ben Goldstein]

(whoops, sorry for the duplicate email, forgot to respond on-list)

Hi Gates,

I think you're right that nimbleEcology's dNmixture_BBP_* functions use this parameterization. You could take a look at the source code for those functions. Internally, we convert from the p/rho (what I called p/s) parameterization into the alpha/beta parameterization needed for dBetaBinom:

https://github.com/nimble-dev/nimbleEcology/blob/master/R/dNmixture.R

(see lines 577-578).

Hope this helps!

Ben

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[Gates Dupont]

Hi Ben,

This is fantastic, thank you! I'll try to implement it and see how it goes. I really appreciate it!

Best,

Gates