I wasn't paying a lot of attention to the R-squared discussion
that has been going on, but I did just happen to notice a new
reference on the topic that just came out, in case this contributes
to the questions that have been posed here on the list:
Statistics in Medicine
Volume 22, Issue 22 , Pages 3527 - 3541
Research Article
Measuring explained variation in linear mixed effects models
Ronghui Xu *
Department of Biostatistics, Harvard School of Public Health and Dana-Farber
Cancer Institute, 44 Binney Street, Boston, MA 02115, U.S.A.
email: Ronghui Xu ([email protected])
*Correspondence to Ronghui Xu, Department of Biostatistics, Harvard School of
Public Health and Dana-Farber Cancer Institute, 44 Binney Street, Boston, MA
02115, U.S.A.
Keywords
empirical Bayes � explained randomness � Kullback-Leibler information �
predicted random effects � residual sum of squares
Abstract
We generalize the well-known R2 measure for linear regression to linear mixed
effects models. Our work was motivated by a cluster-randomized study conducted
by the Eastern Cooperative Oncology Group, to compare two different versions of
informed consent document. We quantify the variation in the response that is
explained by the covariates under the linear mixed model, and study three types
of measures to estimate such quantities. The first type of measures make direct
use of the estimated variances; the second type of measures use residual sums of
squares in analogy to the linear regression; the third type of measures are
based on the Kullback-Leibler information gain. All the measures can be easily
obtained from software programs that fit linear mixed models. We study the
performance of the measures through Monte Carlo simulations, and illustrate the
usefulness of the measures on data sets.
- JK
--
Jay S. Kaufman, Ph.D
-----------------------------
email: [email protected]
-----------------------------
Department of Epidemiology
UNC School of Public Health
2104C McGavran-Greenberg Hall
Pittsboro Road, CB#7435
Chapel Hill, NC 27599-7435
phone: 919-966-7435
fax: 919-966-2089
-----------------------------
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
