R2 measure in mixed models?

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

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