Brintz Ben, Fuentes Claudio, Madsen Lisa
Department of Statistics, Oregon State University, Corvallis, Oregon, U.S.A.
Biometrics. 2018 Dec;74(4):1512-1518. doi: 10.1111/biom.12913. Epub 2018 Jun 5.
N-mixture models are probability models that estimate abundance using replicate observed counts while accounting for imperfect detection. In this article, we propose an asymptotic approximation to the N-mixture model which efficiently estimates large abundances without the computational limitations of the generalized N-mixture model introduced by Dail and Madsen in 2011. It has been suggested in the literature that N-mixture models do not perform well when counts from the same sites show weak patterns of population dynamics. Our proposed model addresses this issue by using the asymptotic information matrix to diagnose model parameter estimability and to derive parameter standard errors. A simulation study show that this model performs almost as well as the Dail-Madsen Generalized N-mixture model at low abundances and improves on it at higher abundances. We illustrate the procedure using two data sets: the American robin data from Dail and Madsen (2011), and counts of chlamydia cases in the state of Oregon from 2007-2016. The chlamydia data exhibit very large abundances and demonstrate the potential usefulness of the proposed model for disease surveillance data.
N - 混合模型是一种概率模型，它在考虑不完全检测的情况下，利用重复观测计数来估计丰度。在本文中，我们提出了一种N - 混合模型的渐近近似方法，该方法能够有效估计较大的丰度，且不存在2011年戴尔和马德森提出的广义N - 混合模型的计算限制。文献中曾指出，当来自同一地点的计数显示出较弱的种群动态模式时，N - 混合模型的表现不佳。我们提出的模型通过使用渐近信息矩阵来诊断模型参数的可估计性并推导参数标准误差，从而解决了这个问题。一项模拟研究表明，该模型在低丰度时的表现与戴尔 - 马德森广义N - 混合模型相近，而在高丰度时则优于该模型。我们使用两个数据集来说明该过程：来自戴尔和马德森（2011年）的美洲知更鸟数据，以及2007 - 2016年俄勒冈州衣原体病例计数。衣原体数据显示出非常大的丰度，并证明了所提出的模型在疾病监测数据方面的潜在有用性。
