[R] Conservative "ANOVA tables" in lmer

[Manuel Morales]

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.

> 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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