Re: [R] Conservative

From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>
Date: Thu 14 Sep 2006 - 10:21:28 GMT

Gregor Gorjanc <gregor.gorjanc@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}
> }

-- 
   O__  ---- Peter Dalgaard             ุster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)                  FAX: (+45) 35327907

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