Definition
Lawrence Lin has the form of the concordance correlation coefficient as
where and are the means for the two variables and and are the corresponding variances. is the correlation coefficient between the two variables.
This follows from its definition as
When the concordance correlation coefficient is computed on a N-length data set (i.e., two vectors of length N) the form is
where the mean is computed as
and the variance
and the covariance
Whereas the ordinary correlation coefficient (Pearson's) is immune to whether the biased or unbiased versions for estimation of the variance is used, the concordance correlation coefficient is not. In the original article Lin suggested the 1/N normalization, while in another article Nickerson appears to have used the 1/(N-1), i.e., the concordance correlation coefficient may be computed slightly differently between implementations.
Read more about this topic: Concordance Correlation Coefficient
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