Mishra, SK
(2007):
*A Comparative Study of Various Inclusive Indices and the Index Constructed by the Principal Components Analysis.*

Preview |
PDF
MPRA_paper_3377.pdf Download (248kB) | Preview |

## 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.

Item Type: | MPRA Paper |
---|---|

Institution: | North-Eastern Hill University, Shillong (India) |

Original Title: | A Comparative Study of Various Inclusive Indices and the Index Constructed by the Principal Components Analysis |

Language: | English |

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

Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis |

Item ID: | 3377 |

Depositing User: | Sudhanshu Kumar Mishra |

Date Deposited: | 02 Jun 2007 |

Last Modified: | 26 Sep 2019 16:05 |

References: | · Adelman, I. And Morris, C.T. (1967) Society, Politics and Economic Development: A Quantitative Approach, John Hopkins Press, Baltimore. · Booysen, F. (2002) “An overview and evaluation of composite indices of development”, Social Indicators Research, 59(2), pp.115-151. · Bradley, C. (1985) “The Absolute Correlation”, The Mathematical Gazette, 69 (447), pp. 12-17. · Cahill, M.B. and Sánchez, N. (2001) “Using Principal Components to produce an Economic and Social Development Index: An Application to Latin America and the U.S”, Atlantic Economic Journal, 29(3), pp. 311-329. · Jahan, S. (2005) “Measurement of Human Development: Evolution of the Human Development Index” Draft Confidential Paper, http://hdr.undp.org/docs/training/oxford/readings/Jahan_HDI.pdf · Kendall, MG and Stuart, A (1968): The Advanced Theory of Statistics, Charles Griffin & Co. London, vol. 3. pp. 285-299. · Michalos, A. C., Sharpe, A. and Muhajarine, N. (2006) “An Approach to a Canadian Index of Well being”, http://creativecity.ca/cecc/downloads/indicators-2006/Michalos-Sharpe-Muhajarine-Approach-CdnIndex-Wellbeing.pdf · Michalos, A.C. (1980) North American Social Report, Vol. 1: Foundations, Population and Health, D. Reidel, Dordrecht. · Mishra, S.K. and Chopra, A. (1978) "Dimensions of Inter-district Disparities in Levels of Development in MP". Indian Geographical Journal, 53. · Mishra, S.K. and Gaikwad, S.B. (1979) "Impact of Economic Development on Welfare and Living Condition of People of MP". Indian Journal of Regional Science, 11(1). · Mishra, S.K. and Ngullie, M.L. (2003) "Locational Characteristics of Quality of Life in Dimapur Area, Nagaland" in S Singh, et al. (eds) Environment, Locational Decisions and Regional Planning: (Proceedings of International Conference). The Geographical Society of North Eastern Hill Region, Shillong, 2003. · Mishra, S. K. (2006-a) "Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions" SSRN: http://ssrn.com/abstract=933827 · Mishra, S. K. (2006-b) "Global Optimization by Particle Swarm Method: A Fortran Program". SSRN: http://ssrn.com/abstract=921504 · Mishra, S. K. (2007) "Construction of an Index By Maximization of the Sum of its Absolute Correlation Coefficients With the Constituent Variables" SSRN: http://ssrn.com/abstract=989088 · Munda G., Nardo M. (2005), "Constructing consistent composite indicators: the issue of weights," EUR 21834 EN, European Commission. · Nardo M., Saisana M., Saltelli A., Tarantola S., Hoffman A., Giovannini E. (2005) Handbook on constructing composite indicators: methodology and user guide. OECD Statistic Working Papers, OECD, Paris. http://www.oecd.org/findDocument/0,2350,en_2649_201185_1_119684_1_1_1,00.html · OECD (2003) Composite Indicators of Country Performance: A Critical Assessment, DST/IND(2003) 5, Paris. · Pal, M.N. (1975) “Regional Disparities in the Levels of Development in India,” Indian Journal of Regional Science, 6(1). · Saltelli, A. (2007) “Composite indicators between analysis and advocacy”, Social Indicators Research, 81(1), pp. 65-77. · Salzman, J. (2003) “Methodological Choices Encountered in the Construction of Composite Indices of Economic and Social Well-Being”, Center for the Study of Living Standards Ottawa, Ontario, Canada, http://www.csls.ca/events/cea2003/salzman-typol-cea2003.pdf |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/3377 |