Mathematics (Jun 2024)
A Rate of Change and Center of Gravity Approach to Calculating Composite Indicator Thresholds: Moving from an Empirical to a Theoretical Perspective
Abstract
A composite indicator (CI) is the mathematical aggregation of sub-dimension (local) indicators used to provide an overall score for the multidimensional concept being measured. CIs are widely used to assess the benefits or risks in human endeavors, such as by creating life satisfaction indices or disaster risk indicators. One important aspect of the development of CIs is setting up value thresholds for taking action, such as in determining the minimum acceptable level of life satisfaction in a community or the maximum acceptable flood risk value beyond which people should be ordered to evacuate from the area in danger. The analytic hierarchy/network process (AHNP) is widely used for the development of CIs. In a review of 111 AHP/ANP CI studies, fewer than 10% discussed any threshold. This means that about 90% of the developed CIs were theoretically sound but lacked the actionable thresholds necessary to be of practical use. Furthermore, for the few studies that set thresholds, the values were typically set arbitrarily or using inadequate statistical approaches. To address this important concern, this study first discusses the most commonly used approaches to setting up thresholds, as well as their inadequacies, and proposes the development of AHP/ANP CI thresholds using a mathematical approach based on the rate of change and center of gravity (RCCG) concepts. Using this approach, a virtual reference alternative, i.e., a threshold profile (TP) made up of the local thresholds of each indicator, is calculated. The key advantage of the proposed method is that it not only provides a non-arbitrary way to set up a CI threshold; more importantly, it is independent of the data and/or alternatives to be evaluated; that is, a threshold calculated with the proposed approach constitutes an absolute reference value, outside the dataset.
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