A Method of Canonical Correlation Analysis for Ordinal Data

Abstract

A method of canonical correlation analysis is discussed, in which the order of magnitude is constrained among partial regression coefficients. Each variate is qualitative, having some categories which are on an ordinal scale. The problem is to solve a constrained nonlinear optimization problem, in which the objective function is the canonical correlation, and the constraints are linear ones imposed on the partial regression coefficients. Since the problem cannot be solved through a conventional eigenvalue problem, an iterative procedure is adopted with successively solving linear programs. This technique works effectively for some types of canonical correlation analysis.