[R-sig-ME] Coefficient of determination (R^2) when using lme()

John Maindonald john.maindonald at anu.edu.au
Wed Apr 2 00:09:47 CEST 2008

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:

> Dear R.S. Cotter,
> I think that interpretation of R2 is not straightforward and it is  
> area
> of research.. Have a look to
> Xu. Measuring explained variation in linear mixed effects models
> Statist. Med. 2003; 22:3527–3541 (DOI: 10.1002/sim.1572)
> Orelien, J.G., Edwards, L.J., Fixed-effect variable selection in  
> linear
> mixed models using R2 statistics Comput. Statist.
> Data Anal. (2007), doi: 10.1016/j.csda.2007.06.006
> Hope this helps you,
> vito
> R.S. Cotter ha scritto:
>> Dear mixed models users,
>> I have recently started using R, and I have learned to use lme ().
>> Is it possible to interpret coefficient of determination (R^2) when
>> using lme ()?
>> Best Regards
>> R.S. Cotter
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> -- 
> ====================================
> Vito M.R. Muggeo
> Dip.to Sc Statist e Matem `Vianelli'
> Università di Palermo
> viale delle Scienze, edificio 13
> 90128 Palermo - ITALY
> tel: 091 6626240
> fax: 091 485726/485612
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

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