Review of Some Statistical Methods for Constructing Composite Indicators

Abstract

The methodology for the construction process of composite indicators is reviewed in a step-by-step approach ranging from the ex-ante definition of the latent variable that is intended to be measure, through the construction process of the composite indicators. We focus particularly on four aggregations methods in order analayze weighting and aggregation approach, Distance P_2, Principal Component Analysis, Data Envelopment Analysis and Mazziotta-Pareto Index. An empirical comparison among them is provided and the composite indices divergences are shown.

Dealing with weighting scheme in composite indicators: An unsupervised distance-machine learning proposal for quantitative data

“…Indeed, the weighting and aggregation aspects of these techniques have received much criticism in the most recent literature (see Refs. [4,13,15,17].…”

“…(2) selecting a group of variables or single indicators that represent the phenomenon to be studied according to the conceptual framework; (3) normalising the single indicators; (4) weighting and aggregating the normalised indicators using a mathematical method (compensatory, partially compensatory or non-compensatory) and ( 5) validating the composite index [15,21,23,26]. Likewise, to maximise the robustness and validity of a composite indicator, the most appropriate methodological choices must be made in each of the previous steps.…”

“…Unlike other methods (see Ref. [15], DP2 introduces the coefficient factor 1 − R 2 for this purpose. Nevertheless, the coefficient of determination R 2 only detects the linear correlations between single indicators.…”

“…Additionally, the weighting schemes of these methods have serious disadvantages that call into question the veracity of their results. Neither the arithmetic mean nor the geometric mean avoid the redundant or overlapping information of single indicators, and PCA only removes the linear redundant information [4,13,15,24,26].…”

The Use of Information Entropy and Expert Opinion in Maximizing the Discriminating Power of Composite Indicators

“…Much of the specialized literature is focused on improving traditional methods for constructing composite indicators [17,18]. In general, traditional statistical and multicriteria methods for constructing composite indicators fail in some way, especially in the sub-indicators weighting and aggregation process [1,[19][20][21].…”