[R] akaike's information criterion
Prof Brian Ripley
ripley at stats.ox.ac.uk
Thu Sep 13 17:10:29 CEST 2001
On Thu, 13 Sep 2001, Thomas Dick wrote:
> Hello all,
> i hope you don't mind my off topic question. i want to use the Akaike criterion
> for variable selection in a regression model. Does anyone know some basic
> literature about that topic?
There's a book
Sakamoto, Y., Ishiguro, M., and Kitagawa G. (1986). Akaike
Information Criterion Statistics. D. Reidel Publishing Company.
for example. And complete derivations and comments on the whole
family in chapter 2 of
Ripley, B. D. (1996) Pattern Recognition and Neural Networks.
> Especially I'm interested in answers to the following questions:
> 1. Has (and if so how has) the criterion to be modified, if i estimate the
> transformations of the variables too?
Those are extra parameters: add them in (unless the maximum occurs at
a range boundary).
> 2. How is the usage of the criterion if i use dummy variables (for categorical
> data) in the model?
Not at all: that is done for you in creating a regression model.
> 3. does the criterion have only one minimum, or may i assume several local
It's a minimum over a finite set of models. Finite sets have no
concept of local minima. However, one can have several models from which
all one-step changes (suitably defined) increase AIC.
AIC is a very general concept which arose in time series/single
processing (and was published by name in the IEEE Trans on Automatic
Control). It's clear how to define it for regular maximum likelihood
problems (hence the boundary restriction above).
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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