On the Measurement of Concordance Among Variables and Its Application

In educational testing problems, some natural restriction on the coefficients may arise in maximizing the correlation or variance of linear combinations of sets of variables. In this article, two statistics based on restricted principal component and restricted canonical correlation (Das & Sen, 1994) are proposed to measure the intra- and inter-group concordance of variables. We also propose using these statistics as criteria for clustering variables. The analysis of encyclopedia data is provided as an illustration.