[R] lme X lmer results
Dave Atkins
datkins at u.washington.edu
Sat Dec 31 15:40:45 CET 2005
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
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