Type

Journal Article

Authors

Andrew C. Parnell
Gavin M. Siriwardena
Helen Sheridan
Gordon Purvis
Barry J McMahon

Subjects

Mathematics

Topics
bayesian framework generalized model ecological data abundance poisson distribution count data novel application agricultural systems

A novel method for quantifying overdispersion in count data with application to farmland birds (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.
Collections Ireland -> University College Dublin -> School of Agriculture and Food Science
Ireland -> University College Dublin -> College of Science
Ireland -> University College Dublin -> Insight Research Collection
Ireland -> University College Dublin -> Agriculture and Food Science Research Collection
Ireland -> University College Dublin -> College of Health and Agricultural Sciences
Ireland -> University College Dublin -> Mathematics and Statistics Research Collection
Ireland -> University College Dublin -> School of Mathematics and Statistics
Ireland -> University College Dublin -> Institutes and Centres
Ireland -> University College Dublin -> Insight Centre for Data Analytics

Full list of authors on original publication

Andrew C. Parnell, Gavin M. Siriwardena, Helen Sheridan, Gordon Purvis, Barry J McMahon

Experts in our system

1
Andrew Parnell
Maynooth University
Total Publications: 45
 
2
Helen Sheridan
TU Dublin
Total Publications: 38
 
3
Gordon Purvis
University College Dublin
Total Publications: 8
 
4
Barry J. McMahon
University College Dublin
Total Publications: 32