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Multinomial N-Mixture Models for Removal Sampling.

08:00 EDT 12th September 2019 | BioPortfolio

Summary of "Multinomial N-Mixture Models for Removal Sampling."

Multinomial N-mixture models are commonly used to fit data from a removal sampling protocol. If the mixing distribution is negative binomial, the distribution of the counts does not appear to have been identified and practitioners approximate the requisite likelihood by placing an upper bound on the embedded infinite sum. In this paper, the distribution which underpins the multinomial N-mixture model with a negative binomial mixing distribution is shown to belong to the broad class of multivariate negative binomial distributions. Specifically, the likelihood can be expressed in closed form as the product of conditional and marginal likelihoods and the information matrix shown to be block diagonal. As a consequence, the nature of the maximum likelihood estimates of the unknown parameters and their attendant standard errors can be examined and tests of hypothesis of the Poisson against the negative binomial mixing distribution formulated. In addition, appropriate multinomial N-mixture models for datasets which include zero site totals can also be constructed. Two illustrative examples are provided. This article is protected by copyright. All rights reserved.

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This article was published in the following journal.

Name: Biometrics
ISSN: 1541-0420
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