Does the analysis of principal components effectively help in determining actual weights for dimensions of an index? An appraisal in Indian context

Abstract

Weights are generally supposed to indicate the relative importance of a dimension variable to explain a particular dependent variable (i.e., a final index), and these weights can be assigned either through individual value judgment, or by using some relevant techniques based upon relative importance of the indices concerned as revealed from the data. Principal Component Analysis (PCA) is playing a major role in determining weights and this principle is clearly based on the degree of variability of the individual dimension- indices. The more the variability, the more will be the assigned weight. Thus, in PCA, the weights are not supposed to be equal and are determined from factor loadings and Eigen-values. In PCA that indicator receives a higher weight which has a higher variance even if that indicator is not directly and even not strongly indicating higher level of importance. In this research agenda, we are to show some major limitations of the Principal Component Analysis and the present study proposes an alternative method to determine actual weights for the underlying dimensions of Human Development Index and in the way has carried out two empirical studieson HDI components of India for the years 1999-2000 and 2007-08.