[R-sig-ME] R2 measure in mixed models?

[David Duffy]

On Mon, 1 Mar 2010, Juliet Hannah wrote:

> How does one try and summarize the "strength" of a fixed effect in the
> mixed model setting?
>
> It is this question that had led me to try and understand the various
> pseudo R-squares.
>
> I'm curious how others do this (for any definition of strength).
>
> On Fri, Feb 26, 2010 at 10:27 AM, Nick Isaac <njbisaac at googlemail.com> wrote:
>> Thanks for these pertinent comments.
>>
>> I can't comment on the motivation for the original post. I have always felt
>> that a single dimensionless Rsq was fairly meaningless in the context of
>> mixed models.
>>
>> Gelman & Pardoe's formula summarizes the fit at each level in the model
>> separately. This has more intuitive appeal, especially since I tend to fit
>> models containing fixed effects at the group level.
>>>
>>> In other words, what's the purpose?  What aspect of the R^2 for a
>>> linear model are you trying to generalize?
>>>
>>> I'm sorry if I sound argumentative but discussions like this sometimes
>>> frustrate me.  A linear mixed model does not behave exactly like a
>>> linear model without random effects so a measure that may be
>>> appropriate for the linear model does not necessarily generalize.
>>>
>>> In a linear model the R^2 statistic is a dimensionless comparison of
>>> the quality of the current model fit, as measured by the residual sum

I have been following this discussion with great interest, and don't pretend
to have any answers.  But, isn't all this only a problem for a MIXED model?
That is, if you made all your variables random effects, then proportion of
variation due to X (in the given population at the given time, yada yada) 
again becomes meaningful?

In the genetics context, where we are usually interested in the random
effects, the "R2" for a given random effect often does strange things
depending on which fixed effects one conditions on.

Another 2c.  David Duffy

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
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