A Structural Equation Modeling Approach to Canonical Correlation Analysis

Canonical Correlation Analysis (CCA) is a generalization of multiple correlation that examines the relationship between two sets of variables. Spectral decomposition can be applied and canonical correlations and canonical weights are obtained. Anderson (2003) also provided the asymptotic distribution of the canonical weights under normality assumption. In this article, we propose a Structural Equation Modeling (SEM) approach to CCA. Mathematical forms are presented to show the equivalence among these models. The weight matrix is obtained as the inverse of the loading matrix and the variance or standard errors of weights are calculated through the Delta method. Different popular SEM software such as Lavaan, Mplus, EQS are demonstrated to illustrate the application, and the results are compared with those obtained from Anderson's (2003) formula. Related issues are also discussed in the last section.