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Measuring explained variation in linear mixed effects models
Author(s) -
Xu Ronghui
Publication year - 2003
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1572
Subject(s) - covariate , linear regression , mixed model , statistics , linear model , generalized linear mixed model , mathematics , measure (data warehouse) , variation (astronomy) , econometrics , computer science , data mining , physics , astrophysics
We generalize the well‐known R 2 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. Copyright © 2003 John Wiley & Sons, Ltd.