Bayesian hierarchical modelling of continuous non-negative longitudinal data with a spike at zero: An application to a study of birds visiting gardens in winter.
Bayesian hierarchical modelling of continuous non-negative longitudinal data with a spike at zero: An application to a study of birds visiting gardens in winter.
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DOI：
10.1002/bimj.201400081
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发表时间：
2016-03
期刊：
影响因子：
--
通讯作者：
Toms MP
中科院分区：
文献类型：
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作者：
Swallow B;Buckland ST;King R;Toms MP
处理峰值为零的连续数据的方法的发展落后于过度分散或零膨胀计数数据的方法。我们认为纵向生态数据对应的年度平均26周的最大计数的鸟类，因此有效地连续，低于零的界限，但也与离散质量为零。我们开发了一个贝叶斯分层Tweedie回归模型，可以直接容纳这种类型的数据共同的多余的零，同时占空间和时间的相关性。该模型的实施进行马尔可夫链蒙特卡罗（MCMC）框架，使用可逆跳MCMC探索参数和模型空间的不确定性。这种回归建模框架非常灵活，不需要对先验的均值-方差关系做出强有力的假设。它还可以直接解释零处的尖峰，同时很容易适用于其他类型的数据和其他模型公式。虽然相关的研究，如这不能证明因果关系，我们的研究结果表明，在一个鸟类捕食者的增加可能导致其猎物物种之一，在英国访问花园饲养站的数量整体下降。这可能反映了家雀行为的变化，以避免雀鹰经常光顾的喂食站，或者由于雀鹰的增加而导致家雀种群规模的减少。
The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zero‐inflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about mean‐variance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.