[R] Conservative

[Peter Dalgaard]

Gregor Gorjanc <gregor.gorjanc at bfro.uni-lj.si> writes:

> 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? 

At the risk of sticking my foot in it due to not reading the paper
carefully enough: There appears to be two other likelihoods in play,
one traditional one depending on fixed effects and variances and
another depending on fixed effects and BLUPs ("most likely
unobservables"). I think Robinson is talking about the equivalence of
those two.

(and BTW ss=Statistical Science in the ref.)

 
> 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}
> }


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