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Canonical correlation analysis is commonly considered to be a general model for most parametric bivariate and multivariate statistical methods. Because of its capability for handling multiple criteria and multiple predictors simultaneously, canonical correlation analysis has a great deal of appeal and has also enjoyed increasing application in the behavioral sciences. However, it has also been plagued by several serious shortcomings. In particular, researchers have been unable to determine the statistical significance of individual parameter estimates or to relax assumptions of the canonical model that are inconsistent with theory and/or observed data. As a result, canonical correlation analysis has found more application in exploratory research than in theory testing. This paper illustrates how these problems can be resolved by expressing canonical correlation as a special case of a linear structural relations model.
Bagozzi et al. (Thu,) studied this question.