[R] difference between splus and R

[Douglas Bates]

Faheem Mitha <faheem at email.unc.edu> writes:

> On Fri, 7 Apr 2000, Faheem Mitha wrote:
> 
> > 
> > On Fri, 7 Apr 2000, Prof Brian D Ripley wrote:
> >  
> > > (The fits for ran2 give the same statistics, so look both to be REML.) 
> > > You should not be using anova on lme models fitted with REML. Although in
> > > this case they are using the same fixed-effects model and so are on
> > > comparable data, the supporting theory is for ML fits only, AFAIK.
> > 
> > I am only using the prepackaged function anova.lme from the package nlme.
> > If you look at the documentation, you will see that not doing anything
> > unconventional with it. While I am not sure what likelihood ratio
> > statistic is being used (the documentation does not say, but it appears
> > that it is probably REML-based) if it is not a legitimate test, then why
> > is it included in the package?
> 
> I'm replying to my own reply, here. I took a more careful look, and
> apparently there is a problem if you are trying to apply anova to models
> fitted with REML where the fixed effects are different. If you try to do
> this, anova gives you results, but also gives a warning message saying the
> results are not meaningful.
> 
> My understanding is that using anova on lme models fitted with REML is Ok
> as long as the fixed effects are the same.

That has been our experience too.  This is discussed in more detail in
the forthcoming book "Mixed-Effects Models in S and S-PLUS" by Jose
Pinheiro and me.  There are some corrections that could be applied
when comparing difference structures for the variance-covariance of
the random effects.  See
@Article{self:lian:1987,
  author = 	 {S. G. Self and K. Y. Liang},
  title = 	 {Asymptotic properties of maximum likelihood
                  estimators and likelihood ratio tests under
                  nonstandard conditions},
  journal = 	 {Journal of the American Statistical Association},
  year = 	 1987,
  volume =	 82,
  pages =	 {605--610}
}
and also a recent paper by Chris Morrell.  An early version of
Morrell's paper was
@inproceedings{morr:1997,
         Author = {Morrell, Christopher H.},
         Title = {Likelihood Ratio Testing of Variance Components in the Linear
                 Mixed-effects Model Using Restricted Maximum Likelihood},
         Year = 1997,
         Booktitle  = {ASA Proceedings of the Biometrics Section},
         Publisher = {American Statistical Association (Alexandria, VA)},
         Pages = {181--186}
     }
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