Weights and importance in composite indicators: Closing the gap.

Composite indicators are very popular tools for assessing and ranking countries and institutions in terms of environmental performance, sustainability, and other complex concepts that are not directly measurable. Because of the stakes that come with the media attention of these tools, a word of caution is warranted. One common misconception relates to the effect of the weights assigned to indicators during the aggregation process. This work presents a novel series of tools that allow developers and users of composite indicators to explore effects of these weights. First, the importance of each indicator to the composite is measured by the nonlinear Pearson correlation ratio, estimated by Bayesian Gaussian processes. Second, the effect of each indicator is isolated from that of other indicators using regression analysis, and examined in detail. Finally, an optimisation procedure is proposed which allows weights to be fitted to agree with pre-specified values of importance. These three tools together give developers considerable insight into the effects of weights and suggest possibilities for refining and simplifying the aggregation. The added value of these tools are shown on three case studies: the Resource Governance Index, the Good Country Index, and the Water Retention Index.