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A Comparative Study of Various Inclusive Indices and the Index Constructed by the Principal Components Analysis

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Abstract

Construction 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.

Suggested Citation

  • Mishra, SK, 2007. "A Comparative Study of Various Inclusive Indices and the Index Constructed by the Principal Components Analysis," MPRA Paper 3377, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:3377
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    File URL: https://mpra.ub.uni-muenchen.de/3377/1/MPRA_paper_3377.pdf
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    1. Andrea Saltelli, 2007. "Composite Indicators between Analysis and Advocacy," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 81(1), pages 65-77, March.
    2. Mishra, SK, 2003. "Quality of life in Dimapur (India)," MPRA Paper 2609, University Library of Munich, Germany.
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    Cited by:

    1. Nayak, Purusottam & Mishra, SK, 2012. "Efficiency of Pena’s P2 Distance in Construction of Human Development Indices," MPRA Paper 39022, University Library of Munich, Germany.
    2. Raihan, Selim & Ahmed, Mansur, 2016. "Spatial divergence of primary education development in Bangladesh through the lens of Education Development Index (EDI)," MPRA Paper 71177, University Library of Munich, Germany.
    3. Mishra, SK, 2012. "A comparative study of trends in globalization using different synthetic indicators," MPRA Paper 38028, University Library of Munich, Germany.
    4. Sudhanshu K. MISHRA, 2016. "BA Note on Construction of a Composite Index by Optimization of Shapley Value Shares of the Constituent Variables," Turkish Economic Review, KSP Journals, vol. 3(3), pages 466-472, September.
    5. 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.
    6. repec:spr:soinre:v:132:y:2017:i:3:d:10.1007_s11205-016-1341-2 is not listed on IDEAS
    7. Mishra, SK, 2012. "A maximum entropy perspective of Pena’s synthetic indicators," MPRA Paper 37797, University Library of Munich, Germany.
    8. Pavel Grigoriev & Olga Grigorieva, 2011. "Self-perceived health in Belarus: Evidence from the income and expenditures of households survey," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(23), pages 551-578, April.
    9. Mishra, SK, 2012. "Construction of Pena’s DP2-based ordinal synthetic indicator when partial indicators are rank scores," MPRA Paper 39088, University Library of Munich, Germany.
    10. Matteo Mazziotta & Adriano Pareto, 2016. "On The Construction Of Composite Indices By Principal Components Analysis," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 70(1), pages 103-109, January-A.
    11. Mishra, SK, 2007. "A Note on Human Development Indices with Income Equalities," MPRA Paper 3513, University Library of Munich, Germany.
    12. Bin, Peng, 2015. "Regional Disparity and Dynamic Development of China: a Multidimensional Index," MPRA Paper 61849, University Library of Munich, Germany.
    13. Mishra, SK, 2007. "Socio-economic Exclusion of Different Religious Communities in Meghalaya," MPRA Paper 3441, University Library of Munich, Germany.
    14. Keshav Sood & Shrabani Mukherjee, 2016. "Triggers and Barriers for ‘Exclusion’ To ‘Inclusion’ in the Financial Sector: A Country-Wise Scrutiny," Working Papers 2016-154, Madras School of Economics,Chennai,India.
    15. Nathaniel Karp & Boyd Nash-Stacey, 2015. "Technology, Opportunity & Access: Understanding Financial Inclusion in the U.S," Working Papers 1525, BBVA Bank, Economic Research Department.

    More about this item

    Keywords

    Principal components analysis; weighted linear combination; aggregation; composite index; egalitarian; inclusive; elitist; representation; under-developed systems;

    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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