A novel method for quantifying overdispersion in count data with application to farmland birds

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Title: A novel method for quantifying overdispersion in count data with application to farmland birds
Authors: McMahon, Barry J.
Purvis, Gordon
Sheridan, Helen
Siriwardena, Gavin M.
Parnell, Andrew C.
Permanent link: http://hdl.handle.net/10197/9383
Date: Apr-2017
Abstract: The statistical modelling of count data permeates the discipline of ecology. Such data often exhibit overdispersion compared with a standard Poisson distribution, so that the variance of the counts is greater than that of the mean. Whereas modelling to reveal the effects of explanatory variables on the mean is commonplace, overdispersion is generally regarded as a nuisance parameter to be accounted for and subsequently ignored. Instead, we propose a method that models the overdispersion as a biologically interesting property of a data set and show how novel inference is provided as a result. We adapted the double hierarchical generalized linear model approach to create an easily extendible model structure that quantifies the influence of explanatory variables on the overdispersion of count data, and apply it to farmland birds. These data were from a study within Irish agricultural ecosystems, in which total bird species abundance and the abundance of farmland indicator species were compared on dairy and non-dairy farms in the winter and breeding seasons. In general, overdispersion in bird counts was greater on dairy farms than on non-dairy farms, and for total bird numbers, overdispersion was greatest on dairy farms in winter. Our code is fitted using the Bayesian package Rstan, and we make all code and data available in a GitHub repository. Within a Bayesian framework, this approach facilitates a meaningful quantification of the effects of categorical explanatory variables on any response variable with a tendency to overdispersion that has a meaningful biological or ecological explanation.
Type of material: Journal Article
Publisher: Wiley
Copyright (published version): 2016 British Ornithologists' Union
Keywords: AbundanceAgricultural systemsBayesian frameworkEcological data
DOI: 10.1111/ibi.12450
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection
Insight Research Collection
Agriculture and Food Science Research Collection

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