Zhu Jun, Eickhoff Jens C, Kaiser Mark S
Department of Statistics, University of Wisconsin-Madison, USA.
Biometrics. 2003 Dec;59(4):955-61. doi: 10.1111/j.0006-341x.2003.00110.x.
Beta-binomial models are widely used for overdispersed binomial data, with the binomial success probability modeled as following a beta distribution. The number of binary trials in each binomial is assumed to be nonrandom and unrelated to the success probability. In many behavioral studies, however, binomial observations demonstrate more complex structures. In this article, a general beta-binomial-Poisson mixture model is developed, to allow for a relation between the number of trials and the success probability for overdispersed binomial data. An EM algorithm is implemented to compute both the maximum likelihood estimates of the model parameters and the corresponding standard errors. For illustration, the methodology is applied to study the feeding behavior of green-backed herons in two southeastern Missouri streams.
贝塔二项式模型广泛应用于过度分散的二项式数据，其中二项式成功概率被建模为服从贝塔分布。假设每个二项式中的二元试验次数是非随机的，且与成功概率无关。然而，在许多行为研究中，二项式观测显示出更复杂的结构。在本文中，开发了一种通用的贝塔二项式 - 泊松混合模型，以考虑试验次数与过度分散的二项式数据的成功概率之间的关系。实现了一种期望最大化（EM）算法来计算模型参数的最大似然估计值和相应的标准误差。为了说明，该方法被应用于研究密苏里州东南部两条溪流中绿背苍鹭的觅食行为。
