beta-binomial dynamic N-mixture model - insufficient data or error in specification?

[Quresh Latif]

Hi all. I am working with a count dataset for Black Swift at waterfalls. I've got data from 128 waterfall sites, 3 years, and 2-3 visits per year, with not all sites surveyed every year. I fit a dynamic N-mixture hurdle model with zero-truncated Poisson error on abundance at occupied sites and binomial error on occupancy (model_OCPAG_pBinYr.nimble). The 5 fundamental parameters for this model are initial occupancy, colonization, extirpation, initial abundance (at occupied sites), and exponential population growth (at occupied sites), with covariates on all 5 and binomial detection probability. The model fit is OK, but there's definitely some lack of fit; the plot below shows observed vs posterior predictive simulated counts. A (zero-truncated) negative binomial version of this model does not improve fit very much. I tried specifying detection probability with a beta-binomial error term (see model_OCPAG_pBB.nimble) with no luck - sampling for many of the parameters fails (Rhat = Inf with Nimble; see Bad_pars_model_OCPAG_pBB.csv). My guess (informed somewhat by a conversation with chatGPT) is that I simply don't have sufficient data to support my model with extra-binomial variability in detection probability modeled as a beta-binomial distribution, but I thought I'd check here to see if anyone has alternative ideas before giving up on this model. Has anyone worked with a beta-binomial detection model, and if so (or regardless) would you give up on the model at this point, or is there anything more you would try to shore up fit (other than adding covariates, which we don't have at the moment).

Quresh S. Latif
Biometrician

Bird Conservancy of the Rockies

230 Cherry St., Ste. 150, Fort Collins, CO 80521

970-482-1707 (ext. 15)

Connecting people, birds and land

www.birdconservancy.org

[Matthijs Hollanders]

Hey,

I’m on my phone so can’t open your files unfortunately. But usually when beta binomial or negative binomial fails when their “base models” don’t, it’s because the introduction of the additional dispersion parameters break identifiability. I’ll be keen to take a look when I can. 

Cheers,

Matt

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