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Ecological StatisticsContemporary theory and application$
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Gordon A. Fox, Simoneta Negrete-Yankelevich, and Vinicio J. Sosa

Print publication date: 2015

Print ISBN-13: 9780199672547

Published to Oxford Scholarship Online: April 2015

DOI: 10.1093/acprof:oso/9780199672547.001.0001

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Mixture models for overdispersed data

Mixture models for overdispersed data

Chapter:
12 Mixture models for overdispersed data
Source:
Ecological Statistics
Author(s):

Jonathan R. Rhodes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199672547.003.0013

Ecological data often do not conform to the assumptions of standard probability distributions and this has important implications for the validity of statistical inference. A common reason for this is that the variability of ecological data is often much higher than can be accounted for by the standard probability distributions that underpin most statistical inference in ecology. This leads to an underestimation of variances and bias in statistical tests unless the overdispersion is accounted for. Consequently, having methods for dealing with overdispersion is an essential component of the ecologist’s statistical toolbox. This chapter introduces statistical methods known as mixture models that can deal with overdispersion. Mixture models are powerful because not only can they account for overdispersion, but they can also help to identify the actual ecological or observation processes that drive overdispersion. The chapter begins by discussing the causes and consequences of overdispersion in ecological data and how overdispersion can be identified. Mixture models are then described and illustrated using two different case studies from survival analysis and the analysis of population abundance. The chapter ends with a discussion of some of the limitations of mixture models and pitfalls to look out for.

Keywords:   continuous mixture model, countable mixture model, finite mixture model, mixture model, observation error, overdispersion, abundance estimation, survival analysis, zero-inflation

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