Efficiency of Pena’s P2 Distance in Construction of Human Development Indices

Abstract

The paper is an attempt to evaluate the efficiency of Pena's DP-2 method over a host of methods used to make composite indices.

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“…Moreover, this method is considered more robust than traditional methods such as PCA and DEA, as demonstrated by Somarriba and Pena (2009). The DP2 distance synthetic indicator also has many properties: non-negativity, commutativity, triangular inequality, existence, determination, monotony, uniqueness, transitivity, invariance to change of origin and/or scale of units in which the variables are defined, invariance to a change in the general conditions and exhaustiveness and reference base (Nayak and Mishra, 2012) (Table I).…”

“…Thus, the weights assigned to a variable depend on its position in the order, making DP2-based composite synthetic indices indeterminate and arbitrary (Montero et al , 2010). It is worth noting that the weights assigned to a variable will depend on its position in the order, making DP2-based composite synthetic indices indeterminate and arbitrary (Nayak and Mishra, 2012). Montero et al (2010) try to suggest the following procedure to solve the indeterminacy problem: Initialize the weight vector, w i = 1 ∀ i = 1, 2, ..., m and define ε = 0.00001. Define ∂ i j = ( d i j / σ i ) ∀ i = 1,2, ..., m and j = 1,2, ..., n . Obtain normalDF j = ∑ j = i m [ ( d i j / σ i ) w i ] ; j = 1, 2, ..., n . Compute Karl Pearson’s coefficient of correlation r( DF ,∂ i ) between DF and ∂ i ∀ i = 1,2, ..., m .…”

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“…Unlike the composite indices discussed so far which are based on the one or the other measure of correlation and maximization of the sum of squared coefficients of that kind of correlation between the composite index and the indicator variables, the last composite index (Pena) is based on Pena's measure of distance (Somarriba and Pena, 2009;Nayak and Mishra, 2012) defined as:…”

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“…(c) Pena method (also known as the P2 distance or DP2 method): The method was proposed by Peña (1977). The application of DP2 has been increasing (Nayak and Mishra 2012), particularly since Somarriba and Pena (2009) conducted their study using DP2 and criticised both principal component analyses and data envelopment analyses. On the other hand some refinement to the method have been suggested (Montero et al 2010).…”

“…This construction solves a large number of problems, for instance, aggregating variables expressed in different units of measurement, arbitrary weights, missing values, and duplicate information (Montero et al 2010;Peña 1977;Somarriba and Pena 2009). Nevertheless, it has several desirable properties: non-negativity, commutativity, triangular inequality, existence, determination, monotony, uniqueness, transitivity, invariance to change of origin and/or scale of units in which the variables are defined, invariance to changes in general conditions, exhaustiveness, and reference base (Nayak and Mishra 2012). We, therefore, aggregated the four indicators using the DP2 method.…”