On the coefficient of determination for mixed regression models |
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Authors: | Ola Hössjer |
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Institution: | Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden |
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Abstract: | 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, since it excludes noise variance (which can never be explained) and thus has one as a natural upper bound. |
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Keywords: | Coefficient of determination Explained variance Individual variance Mixed regression models Noise variance Variance decomposition |
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