extractAIC {base} | R Documentation

## Extract AIC from a Fitted Model

### Description

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

### Usage

    extractAIC    (fit, scale,     k = 2, ...)
    extractAIC.lm (fit, scale = 0, k = 2, ...)
    extractAIC.glm(fit, scale = 0, k = 2, ...)
    extractAIC.aov(fit, scale = 0, k = 2, ...)
    extractAIC.coxph  (fit, scale, k = 2, ...)
    extractAIC.negbin (fit, scale, k = 2, ...)
    extractAIC.survreg(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`.
`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

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 parameters for usual parametric models) of `fit`.

For generalized linear models (i.e., for `lm`, `aov`, and `glm`), -2log L is the deviance, as computed by `deviance(fit)`, plus a constant.

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

For further information, particularly about `scale`, see `step`.

### Value

A numeric vector of length 2, giving

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

### Note

These functions are used in `add1`, `drop1` and `step` and that may be their main use.

### Author(s)

B. D. Ripley

### References

Venables, W. N. and Ripley, B. D. (1997) Modern Applied Statistics with S-PLUS. New York: Springer (2nd ed).

### See Also

`deviance`, `add1`, `step`

### Examples

    example(glm)
    extractAIC(glm.D93)#>>  5  15.129

[Package Contents]