Select the method or formula of your choice.

Different models have different link functions. To calculate the prediction, invert the link function for the model. The inverse functions are in this table.

Model | Link Function | Formula for Prediction |
---|---|---|

Binomial | Logit | |

Binomial | Normit | |

Binomial | Gompit | |

Poisson | Natural log | |

Poisson | Square root | |

Poisson | Identity |

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

exp(·) | the exponential function |

Φ(·) | the cumulative distribution function of the normal distribution |

X' | the transpose of the vector of points to predict for |

the vector of estimated coefficients |

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

Φ | 1, for the binomial and Poisson models |

x_{h} | the vector of a new design point |

the transpose of x_{h} | |

X | the design matrix |

W | the weight matrix |

the first derivative of the link function evaluated at | |

the predicted mean response |

The confidence limits use the Wald approximation method. This is the formula for a 100(1 − *α*)% two-sided confidence interval:

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

the inverse of the link function evaluated at x | |

the transpose of the vector of the predictors | |

the vector of estimated coefficients | |

the value of the inverse cumulative distribution function for the normal distribution evaluated at | |

α | the significance level |

X | the design matrix |

W | the weight matrix |

1, for binomial and Poisson models |