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A note on the ordinal canonical correlation analysis of two sets of ranking scores

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Abstract

In this paper we have proposed a method to conduct the ordinal canonical correlation analysis (OCCA) that yields ordinal canonical variates and the coefficient of correlation between them, which is analogous to (and a generalization of) the rank correlation coefficient of Spearman. The ordinal canonical variates are themselves analogous to the canonical variates obtained by the conventional canonical correlation analysis (CCCA). Our proposed method is suitable to deal with the multivariable ordinal data arrays. Our examples have shown that in finding canonical rank scores and canonical correlation from an ordinal dataset, the CCCA is suboptimal. The OCCA suggested by us outperforms the conventional method. Moreover, our method can take care of any of the five different schemes of rank ordering. It uses the Particle Swarm Optimizer which is one of the recent and prized meta-heuristics for global optimization. The computer program developed by us is fast and accurate. It has worked very well to conduct the OCCA.

Suggested Citation

  • Mishra, SK, 2009. "A note on the ordinal canonical correlation analysis of two sets of ranking scores," MPRA Paper 12796, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:12796
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    File URL: https://mpra.ub.uni-muenchen.de/12796/1/MPRA_paper_12796.pdf
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    References listed on IDEAS

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    1. Korhonen, Pekka & Siljamaki, Aapo, 1998. "Ordinal principal component analysis theory and an application," Computational Statistics & Data Analysis, Elsevier, vol. 26(4), pages 411-424, February.
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    Cited by:

    1. Sudhanshu K MISHRA, 2009. "Representation-Constrained Canonical Correlation-Analysis: A Hybridization Of Canonical Correlation And Principal Component Analysis," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 4(1(7)_ Spr).

    More about this item

    Keywords

    Ordinal; Canonical correlation; rank order; rankings; scores; standard competition; modified competition; fractional; dense; Repulsive Particle Swarm; global optimization; computer program; FORTRAN;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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