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
Multivariate statisticsMathematicsUnivariateCanonical correlationMultivariate analysisStatisticsInvariant (physics)CorrelationRandom variableMultivariate normal distributionEconometrics
Affiliated Institutions
Related Publications
Minimum redundancy feature selection from microarray gene expression data
Selecting a small subset of genes out of the thousands of genes in microarray data is important for accurate classification of phenotypes. Widely used methods typically rank gen...
Uncertainty Principles and Signal Recovery
The uncertainty principle can easily be generalized to cases where the “sets of concentration” are not intervals. Such generalizations are presented for continuous and discrete-...
A Linear Spatial Correlation Model, with Applications to Positron Emission Tomography
Abstract A simple spatial-correlation model is presented for repeated measures data. Correlation between observations on the same subject is assumed to decay as a linear functio...
Generalized Collinearity Diagnostics
Abstract Working in the context of the linear model y = Xβ + ε, we generalize the concept of variance inflation as a measure of collinearity to a subset of parameters in β (deno...
An Application of Multivariate Analysis to Complex Sample Survey Data
Abstract This article adapts a standard method of multivariate analysis to a highly complex sampling design utilizing the method of balanced repeated replication for calculating...
Publication Info
- Year
- 1979
- Type
- article
- Volume
- 44
- Issue
- 1
- Pages
- 43-54
- Citations
- 144
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
144
OpenAlex
Cite This
Elliot M. Cramer,
W. Alan Nicewander
(1979).
Some Symmetric, Invariant Measures of Multivariate Association.
Psychometrika
, 44
(1)
, 43-54.
https://doi.org/10.1007/bf02293783
Identifiers
- DOI
- 10.1007/bf02293783