A Beta-Bernoulli composite index

Recent studies highlight the need for composite indices capable of integrating individual component indicators (or simply indicators) with expert opinions. To address this challenge, we propose a method for constructing composite indices that incorporates expert opinions in a fully endogenous manner through a Beta-Bernoulli process. The process parameters determine the performance of each unit in the phenomenon of interest across the different indicators. These parameters are estimated from the observed indicator values, which are scaled using expert opinion-based goalposts, independently of the units under consideration. The composite index is obtained as the mean of the Beta-Bernoulli variables, but penalised for the degree to which they deviate from the mean—captured in this model by their correlation. By varying the goalposts, the approach enables identification of which indicators play a crucial role in improving the composite index—namely, in improving unit performance—thus providing an effective monitoring tool.