Select the method or formula of your choice.

Deviance measures the discrepancy between the current model and the full model. The full model is the model that has *n* parameters, one parameter per observation. The full model maximizes the log-likelihood function. The full model provides a point of comparison for models with fewer than *n* parameters. Comparisons to the full model use the scaled deviance.

The contribution to the scaled deviance from each individual data point depends on the model.

Model | Deviance |
---|---|

Binomial | |

Poisson |

The degrees of freedom for the test depend on the sample size and the number of terms in the model:

Term | Description |
---|---|

L _{f} | the log-likelihood for the full model |

L_{c} | the log-likelihood of the model with a subset of terms from the full model |

y _{i} | the number of events for the i^{th} row in the data |

the estimated mean response for the i^{th} row in the data | |

m_{i} | the number of trials for the i^{th} row in the data |

n | the number of rows in the data |

p | the regression degrees of freedom |

The generalized Pearson chi-square statistic assesses the relative difference between the observed and fitted values.

The degrees of freedom for the test depend on the sample size and the number of terms in the model. The Pearson statistic has an exact chi-square distribution for normal data. For non-normal data, like the binomial distribution and the Poisson distribution, the statistic approaches the distribution asymptotically.

Term | Description |
---|---|

n | the number of rows in the data |

p | the regression degrees of freedom |

y_{i} | the response value for the i^{th} factor/covariate pattern |

the estimated mean response of the i^{th} row | |

V(·) | the variance function for the model, defined below |

The variance function depends on the model:

Model | Variance function |
---|---|

Binomial | |

Poisson |