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overdispersion
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(Definition)
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When applying the generalized linear model or GLM to the real world, a phenomenon called overdispersion occurs when the observed variance 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, predicted variance = predicted mean(1- predicted mean).
A parameter, called the dispersion parameter,  , 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 distributions from the exponential family are listed in the following table:
- 1
- J. M. Hilbe, Negative Binomial Regression, Cambridge University Press, Cambridge (2007).
- 2
- A. Agresti, An Introduction to Categorical Data Analysis, Wiley & Sons, New York (1996).
- 3
- P. McCullagh and J. A. Nelder, Generalized Linear Models, Chapman & Hall/CRC, 2nd ed., London (1989).
- 4
- A. J. Dobson, An Introduction to Generalized Linear Models, Chapman & Hall, 2nd ed. (2001).
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"overdispersion" is owned by CWoo.
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(view preamble)
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dispersion parameter |
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Cross-references: exponential family, distributions, density function, inclusion, parameter, logistic regression, binary, mean, regression model, variance, real, generalized linear model
There is 1 reference to this entry.
This is version 7 of overdispersion, born on 2004-07-29, modified 2008-03-07.
Object id is 6047, canonical name is Overdispersion.
Accessed 9479 times total.
Classification:
| AMS MSC: | 62J12 (Statistics :: Linear inference, regression :: Generalized linear models) |
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Pending Errata and Addenda
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![$\displaystyle f_{Y_i}(y_i\mid\theta_i)=\operatorname{exp}[\frac{y\theta_i-b(\theta_i)}{a(\phi)}+c(y,\phi)]$](http://images.planetmath.org:8080/cache/objects/6047/l2h/img2.png "$\displaystyle f_{Y_i}(y_i\mid\theta_i)=\operatorname{exp}[\frac{y\theta_i-b(\theta_i)}{a(\phi)}+c(y,\phi)]$")
