Maximum Likelihood and Generalized Linear Models
Maximum Likelihood and Generalized Linear Models
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
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .
