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- Title
Variability explained by covariates in linear mixed-effect models for longitudinal data.
- Authors
Hu, Bo; Shao, Jun; Palta, Mari
- Abstract
Variability explained by covariates or explained variance is a well-known concept in assessing the importance of covariates for dependent outcomes. In this paper we study R² statistics of explained variance pertinent to longitudinal data under linear mixed-effect models, where the R² statistics are computed at two different levels to measure, respectively, within- and between-subject variabilities explained by the covariates. By deriving the limits of R² statistics, we find that the interpretation of explained variance for the existing R² statistics is clear only in the case where the covariance matrix of the outcome vector is compound symmetric. Two new R² statistics are proposed to address the effect of time-dependent covariate means. In the general case where the outcome covariance matrix is not compound symmetric, we introduce the concept of compound symmetry projection and use it to define level-one and level-two R² statistics. Numerical results are provided to support the theoretical findings and demonstrate the performance of the R² statistics.
- Subjects
ANALYSIS of covariance; STATISTICS; MATHEMATICAL models; REGRESSION analysis; MATHEMATICS
- Publication
Canadian Journal of Statistics, 2010, Vol 38, Issue 3, p352
- ISSN
0319-5724
- Publication type
Article
- DOI
10.1002/cjs.10074