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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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Maximum Likelihood and Generalized Linear Models

Maximum Likelihood and Generalized Linear Models

Chapter:
(p.113) 8 Maximum Likelihood and Generalized Linear Models
Source:
The New Statistics with R
Author(s):

Andy Hector

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198729051.003.0008

This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with the generalized linear model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.

Keywords:   maximum likelihood, link functions, variance functions, linear predictors, Box–Cox transformation, gamma distribution

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