Maximum likelihood estimation for N-mixture models.

Abstract:

:The focus of this article is on the nature of the likelihood associated with N-mixture models for repeated count data. It is shown that the infinite sum embedded in the likelihood associated with the Poisson mixing distribution can be expressed in terms of a hypergeometric function and, thence, in closed form. The resultant expression for the likelihood can be readily computed to a high degree of accuracy and is algebraically tractable. Specifically, the likelihood equations can be simplified to some advantage, the concentrated likelihood in the probability of detection formulated and problematic cases identified. The results are illustrated by means of a simulation study and a real world example. The study is extended to N-mixture models with a negative binomial mixing distribution and results similar to those for the Poisson case obtained. N-mixture models with mixing distributions which accommodate excess zeros and, separately, with a beta-binomial distribution rather than a binomial used to model the intra-site counts are also investigated. However the results for these settings, while computationally attractive, do not provide insight into the nature of the maximum likelihood estimates.

journal_name

Biometrics

journal_title

Biometrics

authors

Haines LM

doi

10.1111/biom.12521

subject

Has Abstract

pub_date

2016-12-01 00:00:00

pages

1235-1245

issue

4

eissn

0006-341X

issn

1541-0420

journal_volume

72

pub_type

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