[R] Conservative "ANOVA tables" in lmer

[Andrew Robinson]

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.

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