Advanced Search
MyIDEAS: Login

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

Contents:

Author Info

  • Mishra, SK

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://mpra.ub.uni-muenchen.de/3377/
File Function: original version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3377.

as in new window
Length:
Date of creation: 01 Jun 2007
Date of revision:
Handle: RePEc:pra:mprapa:3377

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC

Related research

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

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Andrea Saltelli, 2007. "Composite Indicators between Analysis and Advocacy," Social Indicators Research, 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. 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.
  2. 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.
  3. Mishra, SK, 2012. "A comparative study of trends in globalization using different synthetic indicators," MPRA Paper 38028, University Library of Munich, Germany.
  4. Mishra, SK, 2007. "Socio-economic Exclusion of Different Religious Communities in Meghalaya," MPRA Paper 3441, University Library of Munich, Germany.
  5. Mishra, SK, 2007. "A Note on Human Development Indices with Income Equalities," MPRA Paper 3513, University Library of Munich, Germany.
  6. Mishra, SK, 2012. "A maximum entropy perspective of Pena’s synthetic indicators," MPRA Paper 37797, University Library of Munich, Germany.
  7. 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.
  8. 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.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:3377. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.