Dealing with Weighting Scheme in Composite Indicators: an Unsupervised Distance-Machine Learning Proposal for Quantitative Data

There is increasing interest in the construction of composite indicators to benchmark units. However, the mathematical approach on which the most commonly used techniques are based does not allow benchmarking in a reliable way. Additionally, the determination of the weighting scheme in the composite indicators remains one of the most troubling issues. Using the vector space formed by all the observations, we propose a new method for building composite indicators: a distance or metric that considers the concept of proximity among units. This approach enables comparisons between the units being studied, which are always quantitative. To this end, we take the P2 Distance method of Pena Trapero as a starting point and improve its limitations. The proposed methodology eliminates the linear dependence on the model and seeks functional relationships that enable constructing the most efficient model. This approach reduces researcher subjectivity by assigning the weighting scheme with unsupervised machine learning techniques. Monte Carlo simulations confirm that the proposed methodology is robust.