Chapter TWELVE. The Generalization to Non-Normal Distributions
Published Online: 11 AUG 2003
DOI: 10.1002/0471467979.ch12
Copyright © 2003 John Wiley & Sons, Inc.
Book Title
Quantitative Methods in Population Health: Extensions of Ordinary Regression
Additional Information
How to Cite
Palta, M. (2003) The Generalization to Non-Normal Distributions, in Quantitative Methods in Population Health: Extensions of Ordinary Regression, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471467979.ch12
Publication History
- Published Online: 11 AUG 2003
- Published Print: 15 AUG 2003
Book Series:
Book Series Editors:
- Walter A. Shewhart,
- Samuel S. Wilks
ISBN Information
Print ISBN: 9780471455059
Online ISBN: 9780471467977
- Summary
- Chapter
Keywords:
- exponential family;
- generalized linear model;
- canonical;
- dispersion;
- binomial;
- Poisson;
- score equation;
- link function;
- variance function;
- likelihood
Summary
We introduce the exponential family of distributions. The canonical and dispersion parameters are defined. Expressions for the mean, variance and score equations as functions of the canonical parameter are provided. Normal, binomial and Poisson distributions are discussed as special cases of exponential family distributions. Linear regression for the canonical parameter is translated into regressions for the mean with canonical links. Equations for estimation with non-canonical links are introduced. Example illustrates using the log link for regression of systolic blood pressure, and contrasts the use of a link function with application of a functional transformation of blood pressure.