Hello everyone,
 
I hope this is a fair enough question, but I don’t have access to a copy
of Bates and Pinheiro. It is probably quite obvious but the answer might
be of general interest.
If I fit a fixed effect with an added quadratic term and then do it as
an orthogonal polynomial using maximum likelihood I get the expected
result- they have the same logLik.
 
mod2a<-lme(wthole~nplants+I(nplants^2),data=d3,random=~1|field/subplot,m
ethod="ML")
mod2b<-lme(wthole~poly(nplants,2),data=d3,random=~1|field/subplot,method
="ML")
 
> anova(mod2a,mod2b)
      Model df      AIC      BIC    logLik
mod2a     1  6 6698.231 6723.869 -3343.116
mod2b     2  6 6698.231 6723.869 -3343.116
 
However if I fit the two models by REML they are not considered to be
the same and I get warned.
 
> anova(mod2a.REML,mod2b.REML)
           Model df      AIC      BIC    logLik
mod2a.REML     1  6 6680.616 6706.219 -3334.308
mod2b.REML     2  6 6666.915 6692.518 -3327.457
 
Warning message: 
Fitted objects with different fixed effects. REML comparisons are not
meaningful. in: anova.lme(mod2a.REML, mod2b.REML) 
 
Well yes, I suppose that’s right, they are not the same fixed effects.
But why does REML give them such different Log likelihoods? And what
should I do if I want to compare a larger set of models. For example the
following, admittedly overparameterised model, can be fitted (slowly) by
either method
 
>mod4<-lme(wthole~poly(nplants,2),data=d3,random=~poly(nplants,2)|field/
subplot,method="ML")
 
But this doesn’t work by either method…
 
>
mod4<-lme(wthole~nplants+I(nplants^2),data=d3,random=~nplants+I(nplants^
2)|field/subplot,method="ML")
 
Error in solve.default(pdMatrix(a, fact = TRUE)) : 
        system is computationally singular: reciprocal condition number
= 2.58558e-045
 
Thanks in advance for clearing up my confusion. The gentler the
explanation, the more useful it would be as far as I am concerned as I
am not a statistician and have to admit I am not at all clear how REML
actually works.
 
Duncan
 
Dr Duncan Golicher
Ecologia y Sistematica Terrestre
Conservación de la Biodiversidad
El Colegio de la Frontera Sur
San Cristobal de Las Casas, Chiapas, Mexico
Tel. 967 1883 ext 9814
dgoliche@sclc.ecosur.mx
 

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