[R] lme X lmer results

[Dave Atkins]

Message: 18
Date: Fri, 30 Dec 2005 12:51:59 -0600
From: Douglas Bates <dmbates at gmail.com>
Subject: Re: [R] lme X lmer results
To: John Maindonald <john.maindonald at anu.edu.au>
Cc: r-help at stat.math.ethz.ch
Message-ID:
	<40e66e0b0512301051i2dc0f257r745c70e749c250f0 at mail.gmail.com>
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On 12/29/05, John Maindonald <john.maindonald at 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 at u.washington.edu