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Re: AIC for split-plot ANOVA

To: Spencer Graves <spencer.graves@pdf.com>
Subject: Re: AIC for split-plot ANOVA
From: Prof Brian Ripley <ripley@stats.ox.ac.uk>
Date: Tue, 17 Feb 2004 16:15:08 +0000 (GMT)
Cc: Christoph Scherber <Christoph.Scherber@uni-jena.de>, <s-news@wubios.wustl.edu>
In-reply-to: <40323238.2090300@pdf.com>
That `model' is actually (probably) three models, one for each error
stratum.  There is no overall likelihood being maximized, and hence no AIC
is even defined.

On Tue, 17 Feb 2004, Spencer Graves wrote:

>       "?lme" says, "See lmeObject for the components of the fit."  The 
> latter reveals that the output includes a component "loglik", from which 
> one can compute the AIC.  Pinheiro and Bates (2000) Mixed-Effects Models 
> in S and S-Plus (Springer) discuss how to use this function, including 
> how to get various types of plots. 
> 
>       hope this helps.  spencer graves

He is calling aov, not lme.  The aov fit is equivalent to an lme REML fit, 
not an lme ML fit which would be needed to compute a value for AIC.

The function AIC will give you a value for a default lme fit, but it is 
not of Akaike's AIC.

> Christoph Scherber wrote:
> 
> > Dear all,
> >
> > is it possible to calculate the Akaike Information Criterion (AIC) for 
> > a split-plot ANOVA model in S-Plus?
> >
> > the model looks like model1_aov(response~factors+Error(Plot/Treatment))
> >
> > Additionally, I´d like to know how to produce diagnostic plots (Q-Q 
> > plots, Residuals etc) for that kind of model.

You do it by stratum: see the examples in MASS (Venables & Ripley, 2002 
and earlier).

-- 
Brian D. Ripley,                  ripley@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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595


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