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Oblique rotaton in canonical correlation analysis reformulated as maximizing the generalized coefficient of determination. (English) Zbl 1285.62135

Summary: To facilitate the interpretation of canonical correlation analysis (CCA) solutions, procedures have been proposed in which CCA solutions are orthogonally rotated to a simple structure. In this paper, we consider oblique rotation for CCA to provide solutions that are much easier to interpret, though only orthogonal rotation is allowed in the existing formulations of CCA. Our task is thus to reformulate CCA so that its solutions have the freedom of oblique rotation. Such a task can be achieved using H. Yanai’s [“Explicit expression of projectors on canonical variables and distances between centroids of groups”, J. Jpn. Stat. Soc. 11, 43–53 (1981)] generalized coefficient of determination for the objective function to be maximized in CCA. The resulting solutions are proved to include the existing orthogonal ones as special cases and to be rotated obliquely without affecting the objective function value, where J. M. F. ten Berge’s [Psychometrika 48, 519–523 (1983; Zbl 0536.62093)] theorems on suborthonormal matrices are used. A real data example demonstrates that the proposed oblique rotation can provide simple, easily interpreted CCA solutions.

MSC:

62P15 Applications of statistics to psychology

Citations:

Zbl 0536.62093
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