Conservative "ANOVA tables" in lmer
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