R2 measure in mixed models?

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