extractAIC {stats} R Documentation

## Extract AIC from a Fitted Model

### Description

Computes the (generalized) Akaike An Information Criterion for a fitted parametric model.

### Usage

```extractAIC(fit, scale, k = 2, ...)
```

### Arguments

 `fit` fitted model, usually the result of a fitter like `lm`. `scale` optional numeric specifying the scale parameter of the model, see `scale` in `step`. Currently only used in the `"lm"` method, where `scale` specifies the estimate of the error variance, and `scale = 0` indicates that it is to be estimated by maximum likelihood. `k` numeric specifying the “weight” of the equivalent degrees of freedom (=: `edf`) part in the AIC formula. `...` further arguments (currently unused in base R).

### Details

This is a generic function, with methods in base R for `"aov"`, `"coxph"`, `"glm"`, `"lm"`, `"negbin"` and `"survreg"` classes.

The criterion used is

AIC = - 2*log L + k * edf,

where L is the likelihood and `edf` the equivalent degrees of freedom (i.e., the number of free parameters for usual parametric models) of `fit`.

For linear models with unknown scale (i.e., for `lm` and `aov`), -2log L is computed from the deviance and uses a different additive constant to `logLik` and hence `AIC`. If RSS denotes the (weighted) residual sum of squares then `extractAIC` uses for - 2log L the formulae RSS/s - n (corresponding to Mallows' Cp) in the case of known scale s and n log (RSS/n) for unknown scale. `AIC` only handles unknown scale and uses the formula n log (RSS/n) - n + n log 2π - sum log w where w are the weights.

For `glm` fits the family's `aic()` function to compute the AIC: see the note under `logLik` about the assumptions this makes.

`k = 2` corresponds to the traditional AIC, using ```k = log(n)``` provides the BIC (Bayesian IC) instead.

### Value

A numeric vector of length 2, giving

 `edf` the “equivalent degrees of freedom” for the fitted model `fit`. `AIC` the (generalized) Akaike Information Criterion for `fit`.

### Note

This function is used in `add1`, `drop1` and `step` and similar functions in package MASS from which it was adopted.

B. D. Ripley

### References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. New York: Springer (4th ed).

`AIC`, `deviance`, `add1`, `step`
```example(glm)