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The New Statistics with RAn Introduction for Biologists$
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Andy Hector

Print publication date: 2015

Print ISBN-13: 9780198729051

Published to Oxford Scholarship Online: March 2015

DOI: 10.1093/acprof:oso/9780198729051.001.0001

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Generalized Linear Models for Data with Non-Normal Distributions

Generalized Linear Models for Data with Non-Normal Distributions

(p.121) 9 Generalized Linear Models for Data with Non-Normal Distributions
The New Statistics with R

Andy Hector

Oxford University Press

This chapter looks at three of the main types of generalized linear model (GLM). GLMs using the Poisson distribution are a good starting place when dealing with integer count data. The default log link function prevents the prediction of negative counts and the Poisson distribution models the variance (approximately equal to the mean). GLMs with a binomial distribution are designed for the analysis of binomial counts (how many times something occurred relative to the total number of possible times it could have occurred). A logistic link function constrains predictions to be above zero and below the maximum using the S-shaped logistic curve. Overdispersion can be diagnosed and dealt with using a quasi-maximum likelihood extension to GLM analysis. Binomial GLMs can also be used to analyse binary data as a special case with some minor differences to the analysis introduced by the constrained nature of the binary data.

Keywords:   GLMs, Poisson distribution, binomial distribution, quasi-likelihood, link functions, variance functions, overdispersion

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