Ordinal Canonical Correlation Analysis


The ordinal canonical correlation coefficient, r(Z1, Z2), is the coefficient of correlation between two ordinal variables (Z1 and Z2), both of them being the composite (ordinal) ranking scores derived from two ordinal multidimensional data sets of ranking scores, X1 and X2, such that r(Z1, Z2) is of the largest magnitude. It may be considered analogous to the conventional coefficient of canonical correlation in which the composite canonical variates (Y1 and Y2) are cardinally measured. It may be noted that while X1 and X2 are in themselves the ordinal variables, their transformation to cardinally measured canonical variates is problematic. Therefore, in such conditions, the ordinal coefficient of correlation (an analog of Spearman's rank correlation) would be a more appropriate measure of concordance between two sets of variables (that is, the ranking scores).

The ordinal canonical correlation analysis (Mishra, 2009) outperforms the conventional canonical analysis in the sense of rank score output. Moreover, this method can take care of any of the five different schemes of rank ordering: ordinal ranking (1-2-3-4 rule), standard competition ranking (1-2-2-4 rule), modified competition ranking (1-3-3-4 rule), dense ranking (1-2-2-3 rule) or fractional ranking (1-2.5-2.5-4 rule). It uses the Particle Swarm Optimizer which is one of the recent and prized meta-heuristics for global optimization. The computer program (source codes) presented here is fast and accurate. It has worked very well to conduct the ordinal canonical correlation analysis.

References :
  • Mishra, S.K. (2009) "A Note on the Ordinal Canonical Correlation Analysis of Two Sets of Ranking Scores", Journal of Quantitative Economics, 7(2), 2009, pp. 173-199. Available at SSRN: Download.

 

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