An R2 statistic for fixed effects in the linear mixed model

Statisticians most often use the linear mixed model to analyze Gaussian longitudinal data. The value and familiarity of the R-2 statistic in the linear univariate model naturally creates great interest in extending it to the linear mixed model. We define and describe how to compute it model R-2 statistic for the linear mixed model by using Only a single model. The proposed R-2 statistic measures multivariate association between the repeated outcomes and the fixed effects in the linear mixed model. The R-2 statistic arises as a 1-1 function of an appropriate F Statistic for testing all fixed effects (except typically the intercept) in a full model. The statistic compares the full model with a null model with all fixed effects deleted (except typically the intercept) while retaining exactly the same covariance structure. Furthermore, the R-2 Statistic leads immediately to a natural definition of a partial R-2 statistic. A mixed model in which ethnicity gives a very small p-value as longitudinal predictor of blood pressure (BP) compellingly illustrates the value of, the statistic. In sharp contrast to the extreme p-value, a very small R-2, a measure of statistical and scientific importance. indicates that ethnicity has in almost negligible association with the repeated BP outcomes for the study. Copyright (C) 2008 John Wiley & Sons, Ltd.