R help - Mar 2008 - Problem comparing Akaike's AIC - nlme package

Hello,

I am comparing models made with nlme functions and non-nlme functions, based
on Akaike's AIC. The AIC values I get for exactly the same model formulation
--for example a linear model with no random effects fit with gls and lm,
respectively-- do not fit, although the values of the four model parameters
are exactly the same. For example:

m1 <- gls(height ~ age, data = Loblolly)
m2 <- lm(height ~ age, data = Loblolly)

m1$coefficients
(Intercept)         age
  -1.312396    2.590523
m2$coefficients
(Intercept)         age
  -1.312396    2.590523

But then:

AIC(m1)
[1] 428.9243
AIC(m2)
[1] 423.9153

I am trying to compare between more complex models, i.e. different ways of
incorporating spatial self-correlation, and this issue with the AIC is
really making me silly!

Thanks,

    S. Begueria

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The problem is that AIC is only defined for ML fitting, and gls defaults 
to REML.

I have always maintained that it is a bug that nlme's logLik function 
returns a log restricted likelihood for the default fits, and that this 
is converted to a mis-named AIC.  If you use

m1 <- gls(height ~ age, data = Loblolly, method="ML")

you wil get agreement.

On Tue, 11 Mar 2008, sbegueria wrote:
>
> Hello,
>
> I am comparing models made with nlme functions and non-nlme functions,
based
> on Akaike's AIC. The AIC values I get for exactly the same model
formulation
> --for example a linear model with no random effects fit with gls and lm,
> respectively-- do not fit, although the values of the four model parameters
> are exactly the same. For example:
>
> m1 <- gls(height ~ age, data = Loblolly)
> m2 <- lm(height ~ age, data = Loblolly)
>
> m1$coefficients
> (Intercept)         age
>  -1.312396    2.590523
> m2$coefficients
> (Intercept)         age
>  -1.312396    2.590523
>
> But then:
>
> AIC(m1)
> [1] 428.9243
> AIC(m2)
> [1] 423.9153
>
> I am trying to compare between more complex models, i.e. different ways of
> incorporating spatial self-correlation, and this issue with the AIC is
> really making me silly!
>
> Thanks,
>
>    S. Begueria
-- 
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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595