Advanced Search
MyIDEAS: Login

Construction of an Index by Maximization of the Sum of its Absolute Correlation Coefficients with the Constituent Variables

Contents:

Author Info

  • Mishra, SK

Abstract

On many occasions we need to construct an index that represents a number of variables. Cost of living index, general price index, human development index, index of level of development, etc are some of the examples that are constructed by a weighted (linear) aggregation of a host of variables. The weights are determined by the importance assigned to the variables to be aggregated. The criterion on which importance of a variable (vis-à-vis other variables) is determined may be varied and usually has its own logic. In many cases the analyst does not have any preferred means or logic to determine the relative importance of different variables. In such cases, weights are assigned mathematically. One of the methods to determine such mathematical weights is the Principal Components analysis. In the Principal Components analysis weights are determined such that the sum of the squared correlation coefficients of the index with the constituent variables is maximized. The method has, however, a tendency to pick up the subset of highly correlated variables to make the first component, assign marginal weights to relatively poorly correlated subset of variables and/or to relegate the latter subset to construction of the subsequent principal components. If one has to construct a single index, such an index undermines the poorly correlated set of variables. The index so constructed is elitist in nature that has a preference to the highly correlated subset over the poorly correlated subset of variables. Further, since there is no dependable method available to obtain a composite index by merging two or more principal components, the deferred set of variables never finds its representation in the further analysis. In this paper we suggest a method to construct an index by maximizing the sum of the absolute correlation coefficients of the index with the constituent variables. We also suggest construction of an alternative index by maximin correlation. Our experiments suggest that the indices so constructed are inclusive or egalitarian. They do not prefer the highly correlated variables much to the poorly correlated variables.

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/3333/
File Function: original version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/3337/
File Function: revised version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3333.

as in new window
Length:
Date of creation: 25 May 2007
Date of revision:
Handle: RePEc:pra:mprapa:3333

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: Index; weighted linear aggregation; principal components; elitist; inclusive; egalitarian; sum of absolute correlation coefficients; maximin correlation; Human development index; cost of living index; level of development index; Differential Evolution; Particle Swarm optimization;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

No references listed on IDEAS
You can help add them by filling out this form.

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, 2007. "A Note on Human Development Indices with Income Equalities," MPRA Paper 3513, 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:3333. 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.