Limitations of Canonical Correlation
- Linear Relationships: CCA assumes that the relationships between variables are linear, which may not always be the case in real-world data.
- Sensitivity to Outliers: CCA can be sensitive to outliers, which can affect the estimation of the canonical correlations and vectors.
- Interpretation of Canonical Variables: While the canonical variables are easy to interpret, interpreting the original variables in terms of these canonical variables can be challenging.
- Assumption of Equal Covariances: CCA assumes that the two sets of variables have equal population covariance matrices, which may not hold true in practice.
- Large Sample Size Requirement: CCA may require a relatively large sample size which is not possible every time.
What is Canonical Correlation Analysis?
Canonical Correlation Analysis (CCA) is an advanced statistical technique used to probe the relationships between two sets of multivariate variables on the same subjects. It is particularly applicable in circumstances where multiple regression would be appropriate, but there are multiple intercorrelated outcome variables. CCA identifies and quantifies the associations among these two variable groups. It computes a set of canonical variates, which are orthogonal linear combinations of the variables within each group, that optimally explain the variability both within and between the groups.