[R] Conservative "ANOVA tables" in lmer

[Andrew Robinson]

On Wed, Sep 13, 2006 at 07:04:17AM -0400, Manuel Morales wrote:
> On Wed, 2006-09-13 at 08:04 +1000, Andrew Robinson wrote:
> > On Tue, September 12, 2006 7:34 am, Manuel Morales wrote:
> > > On Mon, 2006-09-11 at 11:43 -0500, Douglas Bates wrote:
> > >> Having made that offer I think I will now withdraw it.  Peter's
> > >> example has convinced me that this is the wrong thing to do.
> > >>
> > >> I am encouraged by the fact that the results from mcmcsamp correspond
> > >> closely to the correct theoretical results in the case that Peter
> > >> described.  I appreciate that some users will find it difficult to
> > >> work with a MCMC sample (or to convince editors to accept results
> > >> based on such a sample) but I think that these results indicate that
> > >> it is better to go after the marginal distribution of the fixed
> > >> effects estimates (which is what is being approximated by the MCMC
> > >> sample - up to Bayesian/frequentist philosophical differences) than to
> > >> use the conditional distribution and somehow try to adjust the
> > >> reference distribution.
> > >
> > > Am I right that the MCMC sample can not be used, however, to evaluate
> > > the significance of parameter groups. For example, to assess the
> > > significance of a three-level factor? Are there better alternatives than
> > > simply adjusting the CI for the number of factor levels
> > > (1-alpha/levels).
> > 
> > I wonder whether the likelihood ratio test would be suitable here?  That
> > seems to be supported.  It just takes a little longer.
> > 
> > > require(lme4)
> > > data(sleepstudy)
> > > fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
> > > fm2 <- lmer(Reaction ~ Days + I(Days^2) + (Days|Subject), sleepstudy)
> > > anova(fm1, fm2)
> > 
> > So, a brief overview of the popular inferential needs and solutions would
> > then be:
> > 
> > 1) Test the statistical significance of one or more fixed or random
> > effects - fit a model with and a model without the terms, and use the LRT.
> 
> I believe that the LRT is anti-conservative for fixed effects, as
> described in Pinheiro and Bates companion book to NLME.

Yes, you are right.  I had forgotten that.  Back to square one :).
Bert Gunter also kindly pointed this out to me.

Cherse

Andrew


 
> > 2) Obtain confidence intervals for one or more fixed or random effects -
> > use mcmcsamp
> > 
> > Did I miss anything important? - What else would people like to do?
> > 
> > Cheers
> > 
> > Andrew
> > 
> > Andrew Robinson
> > Senior Lecturer in Statistics                       Tel: +61-3-8344-9763
> > Department of Mathematics and Statistics            Fax: +61-3-8344 4599
> > University of Melbourne, VIC 3010 Australia
> > Email: a.robinson at ms.unimelb.edu.au    Website: http://www.ms.unimelb.edu.au
> > 
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-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
Email: a.robinson at ms.unimelb.edu.au         http://www.ms.unimelb.edu.au