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Coefficient of determination (R^2) when using lme()

The question should be: "What is one trying to estimate?"
Or "What is one trying to measure?"  Until that is settled,
no amount of research will go anywhere useful.  Once it
is settled, an answer may be quickly forthcoming.

R^2 ought not to be treated as a quantity that has a magic
that is independent of meaningfulness.  Often, it has no
meaningfulness that is relevant to the intended use of the
regression results.  If used at all adjusted R^2 is preferable
to R^2.

R^2 is a design measure, estimating how effectively
the data are designed to extract a regression signal.
Change the design (e.g., in a linear regression by
doubling the range of values of the explanatory variable),
and one changes (in this case, very substantially
increases) the expected value of R^2.

It can also be used as a rather crude way to compare two
models for the one set of data, i.e., with the same 'design'.
But be careful, replacing y by log(y) can increase R^2
and give a model that fits less well, or vice versa.
Consider why that might be!

What aspect of the 'design' that underpins your multilevel
model do you wish to characterize?

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
On 1 Apr 2008, at 10:54 PM, vito muggeo wrote: