From: Dave Atkins <datkins_at_u.washington.edu>

Date: Sun 01 Jan 2006 - 01:40:45 EST

Date: Sun 01 Jan 2006 - 01:40:45 EST

Message: 18

Date: Fri, 30 Dec 2005 12:51:59 -0600

From: Douglas Bates <dmbates@gmail.com>

Subject: Re: [R] lme X lmer results

To: John Maindonald <john.maindonald@anu.edu.au>
Cc: r-help@stat.math.ethz.ch

Message-ID:

<40e66e0b0512301051i2dc0f257r745c70e749c250f0@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1

On 12/29/05, John Maindonald <john.maindonald@anu.edu.au> wrote:

>> Surely there is a correct denominator degrees of freedom if the design

* >> is balanced, as Ronaldo's design seems to be. Assuming that he has
** >> specified the design correctly to lme() and that lme() is getting the df
** >> right, the difference is between 2 df and 878 df. If the t-statistic
** >> for the
** >> second level of Xvar had been 3.0 rather than 1.1, the difference
** >> would be between a t-statistic equal to 0.095 and 1e-6. In a design
** >> where there are 10 observations on each experimental unit, and all
** >> comparisons are at the level of experimental units or above, df for
** >> all comparisons will be inflated by a factor of at least 9.
*

Doug Bates commented:

I don't want to be obtuse and argumentative but I still am not convinced that there is a correct denominator degrees of freedom for _this_ F statistic. I may be wrong about this but I think you are referring to an F statistic based on a denominator from a different error stratum, which is not what is being quoted. (Those are not given because they don't generalize to unbalanced designs.)

This is why I would like to see someone undertake a simulation study to compare various approaches to inference for the fixed effects terms in a mixed model, using realistic (i.e. unbalanced) examples.

Doug--

Here is a paper that focused on the various alternatives to denominator degrees of freedom in SAS and does report some simulation results:

http://www2.sas.com/proceedings/sugi26/p262-26.pdf

Not sure whether it argues convincingly one way or the other in the present discussion.

cheers, Dave

-- Dave Atkins, PhD datkins@u.washington.edu ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Sun Jan 01 03:04:37 2006

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