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

Listed:
• 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.

## Suggested Citation

• Mishra, SK, 2007. "Construction of an Index by Maximization of the Sum of its Absolute Correlation Coefficients with the Constituent Variables," MPRA Paper 3333, University Library of Munich, Germany.
• Handle: RePEc:pra:mprapa:3333
as

File URL: https://mpra.ub.uni-muenchen.de/3333/1/MPRA_paper_3333.pdf
File Function: original version

File URL: https://mpra.ub.uni-muenchen.de/3337/1/MPRA_paper_3337.pdf
File Function: revised version

## Citations

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Cited by:

1. 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.
2. Mishra, SK, 2007. "A Note on Human Development Indices with Income Equalities," MPRA Paper 3513, University Library of Munich, Germany.

### 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;

### JEL classification:

• C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
• C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

### NEP fields

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