Some Symmetric, Invariant Measures of Multivariate Association
- 1 March 1979
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 44 (1) , 43-54
- https://doi.org/10.1007/bf02293783
Abstract
A distinction is drawn between redundancy measurement and the measurement of multivariate association for two sets of variables. Several measures of multivariate association between two sets of variables are examined. It is shown that all of these measures are generalizations of the (univariate) squared-multiple correlation; all are functions of the canonical correlations, and all are invariant under linear transformations of the original sets of variables. It is further shown that the measures can be considered to be symmetric and are strictly ordered for any two sets of observed variables. It is suggested that measures of multivariate relationship may be used to generalize the concept of test reliability to the case of vector random variables.Keywords
This publication has 11 references indexed in Scilit:
- On redundancy in canonical analysis.Psychological Bulletin, 1976
- MEASURING THE RELATIONSHIP BETWEEN TWO SETS OF VARIABLESBritish Journal of Mathematical and Statistical Psychology, 1974
- A Multivariate Extension of the Correlation RatioEducational and Psychological Measurement, 1974
- A GENERALIZATION OF VECTOR CORRELATION AND ITS RELATION TO CANONICAL CORRELATIONMultivariate Behavioral Research, 1974
- BRIEF REPORT: THE USE OF HIGHLY CORRELATED PREDICTORS IN REGRESSION ANALYSISMultivariate Behavioral Research, 1974
- Canonical Variate Analysis and Related TechniquesReview of Educational Research, 1973
- Measures of Reliability for Profiles and Test BatteriesPsychometrika, 1973
- Bimultivariate Redundancy: A Comprehensive Measure of Interbattery RelationshipMultivariate Behavioral Research, 1971
- Linear Correlations between Sets of VariablesPsychometrika, 1965
- RELATIONS BETWEEN TWO SETS OF VARIATESBiometrika, 1936