# overdispersion

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,

or the binary logistic regression^{} model, where

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

A parameter, called the *dispersion parameter*, $\varphi $, is introducted to the model to lower this overdispersion effect.

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

$${f}_{{Y}_{i}}({y}_{i}\mid {\theta}_{i})=\mathrm{exp}[\frac{y{\theta}_{i}-b({\theta}_{i})}{a(\varphi )}+c(y,\varphi )]$$ |

Dispersion parameters for some of the well known distributions^{} 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 |

\@unrecurse |