Canadian Journal of Statistics

Variability explained by covariates in linear mixed‐effect models for longitudinal data

Journal Article


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. The Canadian Journal of Statistics 38: 352–368; 2010 © 2010 Statistical Society of Canada

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