Using the negative binomial distribution to model overdispersion in ecological count data
Using the negative binomial distribution to model overdispersion in ecological count data
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DOI：
10.1890/10-1831.1
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发表时间：
2011-07-01
期刊：
影响因子：
4.8
通讯作者：
Mantyniemi, Samu
中科院分区：
文献类型：
--
作者：
Linden, Andreas;Mantyniemi, Samu
泊松过程是对生态计数数据围绕理论期望的随机变化进行建模的常用起点。然而，数据通常显示出比泊松分布所暗示的更多的变化。这种过度分散通常是通过使用不同的模型来解释的，这些模型对方差如何随预期变化有不同的假设。这些假设的选择自然会对统计推断产生明显的影响。我们提出了一个参数化的负二项分布，其中两个overdispersion参数被引入到允许各种二次均值-方差关系，包括在最常用的方法中假设的。以鸟类迁徙为例，我们提出了假设的情况下，如何过度分散可能会出现由于采样，群集行为或聚集，环境变化，或这些因素的组合。对于所有考虑的情况下，均值-方差关系可以适当地描述为负二项分布与两个过度分散参数。为了说明这一点，我们将该模型应用于具有高水平过度分散的经验迁移数据，获得了明显不同的模型拟合不同的假设均值-方差关系。所提出的框架可以是一个有用的近似建模的边缘分布的独立计数数据的似然分析。
A Poisson process is a commonly used starting point for modeling stochastic variation of ecological count data around a theoretical expectation. However, data typically show more variation than implied by the Poisson distribution. Such overdispersion is often accounted for by using models with different assumptions about how the variance changes with the expectation. The choice of these assumptions can naturally have apparent consequences for statistical inference. We propose a parameterization of the negative binomial distribution, where two overdispersion parameters are introduced to allow for various quadratic mean-variance relationships, including the ones assumed in the most commonly used approaches. Using bird migration as an example, we present hypothetical scenarios on how overdispersion can arise due to sampling, flocking behavior or aggregation, environmental variability, or combinations of these factors. For all considered scenarios, mean-variance relationships can be appropriately described by the negative binomial distribution with two overdispersion parameters. To illustrate, we apply the model to empirical migration data with a high level of overdispersion, gaining clearly different model fits with different assumptions about mean-variance relationships. The proposed framework can be a useful approximation for modeling marginal distributions of independent count data in likelihood-based analyses.