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 |

Elements of the Pearson chi-square that can be used to detect ill-fitted factor/covariate patterns. Minitab stores the Pearson residual for the *i*^{th} factor/covariate pattern. The formula is:

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

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

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

V | the variance function for the model at |

The variance function depends on the model:

Model |
Variance function |

Binomial | |

Poisson |

A goodness-of-fit test for models with binary responses based on grouping data based on the estimated probabilities. It is the chi-square statistic from a 2 × *g* table of observed and estimated expected frequencies, where *g* is the number of groups. The degrees of freedom for the test is *g* − 2.

The formula is:

To form the groups, Minitab orders the estimated probabilities and then attempts to create 10 groups of equal size.

The expected number of events in a group is:

expected events =

The expected value for the number of nonevents is:

expected nonevents =

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

The number of trials in the k^{th} group | |

o _{k} | The number of events among the factor/covariate patterns |

The average estimated probability for each group | |

π _{i} | The fitted probabilities for the factor/covariate patterns in a group |