[R] Conservative

[Gregor Gorjanc]

Douglas Bates <bates <at> stat.wisc.edu> writes:

> On 9/13/06, Dimitris Rizopoulos <dimitris.rizopoulos <at> med.kuleuven.be>
> > > I believe that the LRT is anti-conservative for fixed effects, as
> > > described in Pinheiro and Bates companion book to NLME.
> > >
> > You have this effect if you're using REML, for ML I don't think there
> > is any problem to use LRT between nested models with different
> > fixed-effects structure.
...
> The other question is how does one evaluate the likelihood-ratio test
> statistic and that is the issue that Dimitris is addressing.  The REML
> criterion is a modified likelihood and it is inappropriate to look at
> differences in the REML criterion when the models being compared have
> different fixed-effects specifications, or even a different
> parameterization of the fixed effects.  However, the anova method for
> an lmer object does not use the REML criterion even when the model has
> been estimated by REML.  It uses the profiled log-likelihood evaluated
> at the REML estimates of the relative variances of the random effects.
>  That's a complicated statement so let me break it down.
...

Is this then the same answer as given by Robinson:1991 (ref at the end) to
question by Robin Thompson on which likelihood (ML or REML) should be used
in testing the "fixed" effects. Robinson answered (page 49 near bottom 
right) that both likelihoods give the same conclusion about fixed effects. 
Can anyone comment on this issues? 

Thanks, Gregor

@Article{Robinson:1991,
  author =       {Robinson, G. K.},
  title =        {That {BLUP} is a good thing: the estimation of random
                  effects},
  journal =      ss,
  year =         {1991},
  volume =       {6},
  number =       {1},
  pages =        {15--51},
  keywords =     {BLUP, example, derivations, links, applications},
  vnos =         {GG}
}