Title: Structural equation modeling and canonical correlation analysis
Authors: Zhenqiu Laura Lu - University of Georgia (United States) [presenting]
Fei Gu - Mcgill University (Canada)
Abstract: Canonical Correlation Analysis (CCA) is a generalization of multiple correlation that examines the relationship between two sets of variables. Traditional methods apply spectral decomposition to obtain canonical correlations and canonical weights. It has also been previously provided the asymptotic distribution of the canonical weights under normality assumption. We propose a new approach by using Structural Equation Modeling (SEM) approach to canonical correlation analysis. Mathematical forms are presented to show the equivalence among these models. Popular SEM software such as Lavaan, Mplus, EQS are demonstrated to illustrate the application. 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. The results obtained from SEM approach are compared with those obtained from traditional CCA approach and also from the Andersons (2003) formula. Advantages of this new approach include that (1) it provides both canonical correlations and the covariances of canonical variates, (2) it is very practically and flexible because existing SEM software can be used. Related issues are also discussed in the last section.