When applying the generalized linear model or GLM to the real world, a phenomenon called overdispersion occurs when the observed varianceMathworldPlanetmath of the data is larger than the predicted variance. This is particularly apparent in the case of a Poisson regression model, where

predicted variance = predicted mean,

or the binary logistic regressionMathworldPlanetmath model, where

predicted variance = predicted mean(1- predicted mean).

A parameter, called the dispersion parameter, ϕ, is introducted to the model to lower this overdispersion effect.

The GLM, with the inclusion of this dispersion parameter, has the following density function:


Dispersion parameters for some of the well known distributionsPlanetmathPlanetmath from the exponential family are listed in the following table:

Title overdispersion
Canonical name Overdispersion
Date of creation 2013-03-22 14:30:34
Last modified on 2013-03-22 14:30:34
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 10
Author CWoo (3771)
Entry type Definition
Classification msc 62J12
Defines dispersion parameter