[R] akaike's information criterion

[Prof Brian Ripley]

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.
     Cambridge.


> 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
> minima?

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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