Canonical Concordance Correlation Analysis

A multivariate technique named Canonical Concordance Correlation Analysis (CCCA) is introduced. In contrast to the classical Canonical Correlation Analysis (CCA) which is based on maximization of the Pearson's correlation coefficient between the linear combinations of two sets of variables, the CCCA maximizes the Lin's concordance correlation coefficient which accounts not just for the maximum correlation but also for the closeness of the aggregates' mean values and the closeness of their variances. While the CCA employs the centered data with excluded means of the variables, the CCCA can be understood as a more comprehensive characteristic of similarity, or agreement between two data sets measured simultaneously by the distance of their mean values and the distance of their variances, together with the maximum possible correlation between the aggregates of the variables in the sets. The CCCA is expressed as a generalized eigenproblem which reduces to the regular CCA if the means of the aggregates are equal, but for the different means it yields a different from CCA solution. The properties and applications of this type of multivariate analysis are described. The CCCA approach can be useful for solving various applied statistical problems when closeness of the aggregated means and variances, together with the maximum canonical correlations are needed for a general agreement between two data sets.

Automated summary

Introduces a multivariate technique called Canonical Concordance Correlation Analysis (CCCA) which maximizes the Lin's concordance correlation coefficient between two sets of variables to measure similarity and agreement. It considers not only the maximum correlation but also the closeness of mean values and variances of the aggregates. CCCA is a generalized eigenproblem that provides a different solution from CCA when the means of the aggregates are different. It has properties and applications for solving applied statistical problems that require closeness of mean values and variances, along with maximum canonical correlations between two data sets.