extractAIC               package: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

