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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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swallow2015biometricalj_earlyview.pdf (446.7Kb)
Date
03/2016
Author
Swallow, Benjamin Thomas
Buckland, Stephen Terrence
King, Ruth
Toms, Mike
Funder
EPSRC
Grant ID
EP/I000917/1
Keywords
Bayesian hierarchical model
Continuous nonnegative data
Excess zeros
Tweedie distributions
QA Mathematics
QH301 Biology
NDAS
BDC
R2C
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Abstract
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.
Citation
Swallow , B T , Buckland , S T , King , R & Toms , M 2016 , ' 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 ' , Biometrical Journal , vol. 58 , no. 2 , pp. 357-371 . https://doi.org/10.1002/bimj.201400081
Publication
Biometrical Journal
Status
Peer reviewed
DOI
https://doi.org/10.1002/bimj.201400081
ISSN
0323-3847
Type
Journal article
Rights
2015 The Author. Biometrical Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/6164

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