Enhancing the comprehensibility of multidimensional phenomena: The optimal-entropy method for constructing composite indicators. A new index to measure the quality of the public health system in the municipalities of Minas Gerais

The analysis of multidimensional phenomena, such as the public health system, poses significant challenges due to the need to integrate and interpret data from different sources and natures, and composite indicators offer an aggregated and simplified view of the multidimensional phenomenon. This article proposes a method for constructing composite indicators using the optimal entropy technique, applied to the evaluation of the quality of the public health system in municipalities in Minas Gerais with more than 30 thousand inhabitants. The focus is on weighting, aiming to maximize the discrimination between the indicators, solving important problems presented by the traditional entropy weighting method. The approach uses the data entropy test and sequential quadratic programming for optimization. The results indicate that the use of linear entropy instead of Shannon entropy in the entropy test increases the variability and discriminant power of the indicators, contributing to a more accurate analysis of the quality of the public health system.