Clarification on multi-trap specification and details$distri

[bgerber]

I am curious as to whether secr uses a multinomial observation model as in Gardener et al. 2009 when specifying for 'multi-trap"? This seems to be implied on page 269 of the Spatial Capture-Recapture book by Royle et al. 2013. However, most of the literature discusses the use of a competing risks model (Borchers and Efford 2008). I have either misunderstood somewhere along the way or have not made the link between the two specifications.

Second, I would appreciate some help in explaining the difference in the specification of - details$distribution = "binomial" vs details$distribution = M, where M is a larger number than the total number of animals detected. If M is a super-population and n is drawn from a binomial with this size, what
is p in this case and how is it related to the psi of fitting Bayesian models via data augmentation.

Thanks!
Sincerely, Brian

Borchers, D. L., & Efford, M. G. (2008). Spatially explicit maximum likelihood methods for capture–recapture studies. Biometrics, 64(2), 377-385.

Gardner, B., Royle, J. A., & Wegan, M. T. (2009). Hierarchical models for estimating density from DNA mark-recapture studies. Ecology, 90(4), 1106-1115.

Royle, J. A., Chandler, R. B., Sollmann, R., & Gardner, B. (2013). Spatial capture-recapture. Academic Press.

[murray.efford]

Brian
1. For detectors of type "multi", 'secr' uses the competing risk model from Borchers & Efford 2008. I haven't seen the book, but Royle et al have reinvented this as a 'multinomial' model. The original term referred to a multi-catch trap as opposed to single-catch trap (other detector types that are not traps allow multiple detections of an individual on one occasion, whereas multi-catch traps allow multiple individuals in the same trap).
2. The option of specifying distribution = M is a quirky addition from when I was researching the behaviour of estimates from data augmentation (Efford 2011 Ecology 92:2202-2207). From memory, for density D, region area A, N = \int_X D(X) dX and M > N, the data-augmentation psi = \int_X D(X) dX / M, and the binomial p = \int_X D(X) p.(X) dX / M, contrasting with the usual binomial form p = \int_X D(X) p.(X) dX / N. Innocent users should be shielded from this stuff!
Murray

[bgerber]

Thanks Dr. Efford, your comment is much appreciated. If you ever take a look at the book, you are cited as personal communication for the multinomial comment being used in secr.

Thanks.
Sincerely, Brian