TWELVE. The Generalization to Non-Normal Distributions

  1. Mari Palta

Published Online: 11 AUG 2003

DOI: 10.1002/0471467979.ch12

Quantitative Methods in Population Health: Extensions of Ordinary Regression

Quantitative Methods in Population Health: Extensions of Ordinary Regression

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

Author Information

  1. Madison, Wisconsin, USA

Publication History

  1. Published Online: 11 AUG 2003
  2. Published Print: 15 AUG 2003

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780471455059

Online ISBN: 9780471467977

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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.