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`. `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 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 `AIC`.

`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.

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)