[R] Degrees of freedom for lm in logLik and AIC

[Rubén Roa]

However, shouldn't _free parameters_ only be counted for degrees of freedom and for calculation of AIC?
The sigma parameter is profiled out in a least-squares linear regression, so it's not free, it's not a dimension of the likelihood.
Just wondering ...

____________________________________________________________________________________ 

Dr. Rubén Roa-Ureta
AZTI - Tecnalia / Marine Research Unit
Txatxarramendi Ugartea z/g
48395 Sukarrieta (Bizkaia)
SPAIN



> -----Mensaje original-----
> De: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] En nombre de Frank Harrell
> Enviado el: lunes, 28 de marzo de 2011 15:44
> Para: r-help at r-project.org
> Asunto: Re: [R] Degrees of freedom for lm in logLik and AIC
> 
> Thank you Peter.  I didn't realize that was the convention used.
> Frank
> 
> 
> Peter Dalgaard-2 wrote:
> > 
> > On Mar 28, 2011, at 05:36 , Frank Harrell wrote:
> > 
> > > I have a question about the computation of the degrees 
> of freedom 
> > in a linear > model:
> > >
> > > x <- runif(20); y <- runif(20) > f <- lm(y 
> ~ x) > 
> > logLik(f) > 'log Lik.' -1.968056 (df=3) > > The 3 
> is coming 
> > from f$rank + 1.  Shouldn't it be f$rank?  This affects > AIC(f).
> > 
> > I count three parameters in a simple linear regression: 
> alpha, beta, 
> > sigma.
> > 
> > From a generic-likelihood point of view, I don't see how 
> you can omit 
> > the last one.
> > 
> > -pd
> > 
> > --
> > Peter Dalgaard
> > Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 
> > 2000 Frederiksberg, Denmark
> > Phone: (+45)38153501
> > Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
> > 
> > ______________________________________________
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> > 
> 
> 
> -----
> Frank Harrell
> Department of Biostatistics, Vanderbilt University
> --
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> Lik-and-AIC-tp3410687p3411759.html
> Sent from the R help mailing list archive at Nabble.com.
> 
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>