12 Canonical Analysis and canals()

12.1 Equations

If there are only two blocks the generalized eigenvalue problem for the Burt matrix becomes $$\begin{bmatrix} D_1&C_{12}\\C_{21}&D_2 \end{bmatrix} \begin{bmatrix} a_1\\a_2 \end{bmatrix}=2\lambda\begin{bmatrix}D_1&0\\0&D_2\end{bmatrix}\begin{bmatrix} a_1\\a_2 \end{bmatrix},$$ which we can rewrite as $$\begin{split} C_{12}a_2&=(2\lambda-1)D_1a_1,\\ C_{21}a_1&=(2\lambda-1)D_2a_2, \end{split}$$ from which we see that MVAOS maximizes the sum of the $r$ largest canonical correlations between $H_1$ and $H_2$. See also Van der Velden (2012).

12.2 Examples

References

Van der Velden, M. 2012. “On Generalized Canonical Correlation Analysis.” In Proceedings 58th World Statistical Congress, 2011, Dublin, 758–65. The Hague: International Statistical Instutute.