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A note on the sub-optimality of rank ordering of objects on the basis of the leading principal component factor scores

By SK Mishra

Abstract

This paper demonstrates that if we intend to optimally rank order n objects (candidates) each of which has m attributes or rank scores awarded by m evaluators, then the ordinal ranking of objects by the conventional principal component based factor scores turns out to be suboptimal. Three numerical examples have been provided to show that principal component based rankings do not necessarily maximize the sum of squared correlation coefficients between the individual m rank scores arrays, X(n,m), and overall rank scores array, Z(n).

Topics: C43 - Index Numbers and Aggregation, C14 - Semiparametric and Nonparametric Methods: General, C63 - Computational Techniques; Simulation Modeling, C87 - Econometric Software, C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Year: 2008
DOI identifier: 10.2139/ssrn.1321369
OAI identifier: oai:mpra.ub.uni-muenchen.de:12419

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