A Comparative Study of Various Inclusive Indices and the Index Constructed by the Principal Components Analysis
AbstractConstruction of (composite) indices by the PCA is very common, but this method has a preference for highly correlated variables to the poorly correlated variables in the data set. However, poor correlation does not entail the marginal importance, since correlation coefficients among the variables depend, apart from their linearity, also on their scatter, presence or absence of outliers, level of evolution of a system and intra-systemic integration among the different constituents of the system. Under-evolved systems often throw up the data with poorly correlated variables. If an index gives only marginal representation to the poorly correlated variables, it is elitist. The PCA index is often elitist, particularly for an under-evolved system. In this paper we consider three alternative indices that determine weights given to different constituent variables on the principles different from the PCA. Two of the proposed indices, the one that maximizes the sum of absolute correlation coefficient of the index with the constituent variables and the other that maximizes the entropy-like function of the correlation coefficients between the index and the constituent variables are found to be very close to each other. These indices alleviate the representation of poorly correlated variables for some small reduction in the overall explanatory power (vis-à-vis the PCA index). These indices are inclusive in nature, caring for the representation of the poorly correlated variables. They strike a balance between individual representation and overall representation (explanatory power) and may perform better. The third index obtained by maximization of the minimal correlation between the index and the constituent variables cares most for the least correlated variable and in so doing becomes egalitarian in nature.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 3377.
Date of creation: 01 Jun 2007
Date of revision:
Principal components analysis; weighted linear combination; aggregation; composite index; egalitarian; inclusive; elitist; representation; under-developed systems;
Find related papers by JEL classification:
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
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- Andrea Saltelli, 2007. "Composite Indicators between Analysis and Advocacy," Social Indicators Research, Springer, vol. 81(1), pages 65-77, March.
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- Mishra, SK, 2012. "A note on construction of heuristically optimal Pena’s synthetic indicators by the particle swarm method of global optimization," MPRA Paper 37625, University Library of Munich, Germany.
- Mishra, SK, 2007. "Socio-economic Exclusion of Different Religious Communities in Meghalaya," MPRA Paper 3441, University Library of Munich, Germany.
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