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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

Research output: Contribution to journalArticle


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.


Original languageEnglish
Pages (from-to)357-371
JournalBiometrical Journal
Issue numberSI
Early online date3 Mar 2015
Publication statusPublished - Mar 2016

    Research areas

  • Bayesian hierarchical model, Continuous nonnegative data, Excess zeros, Tweedie distributions

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