How can you use Canonical Correlation Analysis (CCA) to inform business decisions?

1 What is CCA?

CCA is a method of finding linear combinations of variables from two sets that maximize their correlation. In other words, CCA tries to find the best way to combine variables from one set (such as product quality and service) to create a new variable (such as quality-service index) that is highly correlated with another new variable created from the second set (such as satisfaction-loyalty index). The correlation between these two new variables is called the canonical correlation, and it measures the degree of association between the two sets of variables.

2 How to perform CCA?

To perform CCA, you need two sets of variables that have at least two variables each and are measured on the same units or subjects. For example, ratings of product quality and service from customers, and ratings of satisfaction and loyalty from the same customers. You can use software packages such as R, SPSS, or SAS to obtain outputs like the canonical correlation coefficients which indicate the strength of the relationship between the two sets of variables (the higher the coefficient, the stronger the association). Additionally, you will get canonical loadings which show how each variable contributes to the new variables created by CCA (the higher the loading, the more important the variable is for the new variable). Moreover, you will get canonical cross-loadings which show how each variable correlates with the new variables from the other set (the higher the cross-loading, the more relevant the variable is for other set). Finally, there is a canonical redundancy analysis that measures how much variance in one set of variables is explained by the other set of variables.

5 What are the limitations of CCA?

CCA is a useful and versatile technique, but it also has some limitations to be aware of. For example, it assumes linear relationships, requires large sample sizes, does not imply causality, and may be sensitive to outliers, multicollinearity, or measurement errors. To overcome these issues, you may need to use other techniques or methods, such as nonlinear CCA, partial least squares, or structural equation modeling. This depends on your research questions and data characteristics.