RV Coefficient and Congruence Coefficient

The congruence coefficient was first introduced by Burt (1948) under the name of unadjusted correlation as a measure of the similarity of two factorial configurations. The name congruence coefficient was later tailored by Tucker (1951, see also Harman, 1976). The congruence coefficient is also sometimes called a monotonicity coefficient (Borg & Groenen, 1997, p. 203). The congruence coefficient takes values between −1 and +1. The RV coefficient was introduced by Escoufier (1973, see also Robert & Escoufier, 1976) as a measure of similarity between squared symmetric matrices (specifically: positive semi-definite matrices) and as a theoretical tool to analyze multivariate techniques. The RV coefficient is used in several statistical techniques such as STATIS and DISTATIS (see corresponding entries and Abdi, 2003). In order to compare rectangular matrices using the RV coefficient the first step is to transform them into square matrices. The RV 1In: Neil Salkind (Ed.) (2007). Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. Address correspondence to: Hervé Abdi Program in Cognition and Neurosciences, MS: Gr.4.1, The University of Texas at Dallas, Richardson, TX 75083–0688, USA E-mail: [email protected] http://www.utd.edu/∼herve