Index: Barker 2018 - Reliability of N-Mixture Models

Barker 2018 - Reliability of N-Mixture Models

Routing Summary

Full capture of Barker, Schofield, Link and Sauer (2018), Biometrics 74(1): 369-377, used as the open-access source for the N-mixture topic (Royle 2004 had no legal open PDF reachable). 4 notes.

• Need the paper on one page or the source map? → Barker 2018 - Reliability of N-Mixture Models - Overview
• Need the N-mixture definition, the $L_1{L}_2{L}_3$ decomposition, or the multivariate Poisson? → Barker 2018 - N-Mixture Model and the Capture-Recapture View
• Need why $N$ is not identified under Poisson, or the 82/59/41% discrimination results? → Barker 2018 - Poisson Alternative and Model Discrimination
• Need Poisson regression for relative abundance, the flycatcher Table 2, or the conclusions? → Barker 2018 - Relative Abundance, Alder Flycatcher Example and Discussion

Concept Map

Concept	Note	Type	Depends On	Key Result
N-mixture model	Barker 2018 - N-Mixture Model and the Capture-Recapture View	definition	-	Binomial counts, Poisson $N_i$
Likelihood decomposition Mt, M0	Barker 2018 - N-Mixture Model and the Capture-Recapture View	theorem	capture-recapture	$L_1$ (lost) dominates $L_2{L}_3$
Poisson nonidentifiability	Barker 2018 - Poisson Alternative and Model Discrimination	theorem	Eq. 4	only $\lambda =Np$ estimable
DPLN counterexample and Table 1	Barker 2018 - Poisson Alternative and Model Discrimination	example	moments	competing model chosen/tied 82%, 59%, 41%
Relative abundance Poisson model	Barker 2018 - Relative Abundance, Alder Flycatcher Example and Discussion	definition	partial likelihood	${\alpha }_p,{\alpha }_N$ confounded; ${\beta }_N$ estimable
Flycatcher Table 2	Barker 2018 - Relative Abundance, Alder Flycatcher Example and Discussion	example	models	site effects agree across 4 fits

Notes

• Barker 2018 - Reliability of N-Mixture Models - Overview — CONTAINS: summary, swap rationale for Royle 2004, source map.
• Barker 2018 - N-Mixture Model and the Capture-Recapture View — CONTAINS: model, limitations, Eq. 1, 2, 5, Fig. 1, thinning check.
• Barker 2018 - Poisson Alternative and Model Discrimination — CONTAINS: Eq. 3, 4, 6, DPLN model, Table 1, scenario results, covariance identification.
• Barker 2018 - Relative Abundance, Alder Flycatcher Example and Discussion — CONTAINS: Eq. 7-10, flycatcher models and Table 2, discussion, Python.

Sources

• Barker 2018 - On the Reliability of N-Mixture Models for Count Data — Biometrics 74(1): 369-377, 9 pp.

See Also

• MacKenzie 2002 - Site Occupancy with Imperfect Detection - Overview, Concept - Closed-Population Capture-Recapture and Otis Models, Concept - Marginalising Latent Discrete Counts for HMC.