| The purpose of this study was to explore the relationship between canonical correlation analysis and structural equation modeling. Data were scores of eleven scales from 584 4th and 6th grade students. The study described canonical correlation analysis (CCA) in comparison with structural equation modeling (SEM) by analyzing the same data set.
For canonical correlation analysis, the data contained seven x variables and four y variables. Because the number of canonical function was mathematically limited by the number of variables in the smaller set, the maximum number of canonical function for the data was four. Among the four canonical functions, only the 1st canonical function reached statistical significance. In addition, the analysis not only provided raw and standardized canonical coefficients and redundancy coefficients, but also provided structure coefficients and index coefficients.
Canonical correlation analysis could be represented as a multiple indicator/multiple causes (MIMIC) model. Maximum-likelihood estimates of the model parameters could be generated by the LISREL computer program. The parameter estimates from SEM were the same as those from canonical correlation analysis.
Actually, the representation of CCA as a SEM seemed to be a little complex, because several related models had to be analyzed, and some additional calculations were needed to obtain all the results from CCA. In other words, CCA could be considered as a special case of SEM. In sum, two advantages of the SEM approach to CCA were: (1) significance testing of canonical weights and index coefficients were possible; (2) significance testing for individual canonical correlation functions were possible.