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

Roberts, Kyle kyler at mail.smu.edu
Tue Apr 1 22:21:28 CEST 2008

My $0.02.

Gelman also has an excellent article, but he uses Bayes to estimate explained variance, so it may not be as straightforward as other methods.

[2006] Bayesian measures of explained variance and pooling in multilevel (hierarchical) models. Technometrics, 48(2), 241--251. (Andrew Gelman and Iain Pardoe)

I personally am not a fan of simply correlating the fitted values with the raw scores. The problem, as I see it, is that you ran the multilevel model because you wanted to honor the nesting structure (for any number of reasons). I see doing this almost like when people run ANOVAs as a post hoc for a MANOVA. If your analysis is multilevel, then produce a statistic for understanding explained variance that is also multilevel. By the way, I have come full circle on this. I used to think that we needed a single metric to tell us about explained variance in a model (see http://www.hlm-online.com/papers/). Now, I'm not so sure.

One other problem is that unlike the OLS counterpart, in multilevel analysis you can actually ADD variance to your model through the addition of covariates/predictors. This is often a sign of model misspecification, but it can also occur when the model is correctly specified (and no, group mean centering won't always fix this problem). If you do a search on the multilevel listserv, you can see this discussed in length in multiple threads. You can also see a discussion of this in Snijders & Bosker (1999, p. 99-109)

Hope this helps,

Dr. J. Kyle Roberts
Department of Literacy, Language and Learning
School of Education and Human Development
Southern Methodist University
P.O. Box 750381
Dallas, TX  75275

-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of vito muggeo
Sent: Tuesday, April 01, 2008 6:55 AM
To: cotterrs at gmail.com
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Coefficient of determination (R^2) when using lme()

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,


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

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