On the coefficient of determination for mixed regression models

For mixed regression models, we define a variance decomposition including three terms, explained individual variance, unexplained individual variance and noise variance. In contrast to traditional variance decomposition, it is thus the unexplained  , not the explained, variance that is split. It gives rise to a coefficient of individual determination (CID) defined as the estimated fraction of explained individual variance. We argue that in many applications CID is a valuable complement to R²$R^2$, since it excludes noise variance (which can never be explained) and thus has one as a natural upper bound.