RECONCILING INTERPRETABILITY, INFORMATIONAL AND EXPLANATORY POWER IN COMPOSITE INDICATORS VIA PRINCIPAL COMPONENT ANALYSIS (PCA)

Composite indicators are mathematical tools that assist in understanding complex realities such as poverty, sustainability, and healthcare systems. This study explores the limitations of Principal Component Analysis in reconciling three fundamental elements for representing multidimensional phenomena characterized by weakly intercorrelated data. First, informational power, estimated by the sum of the squared correlations between the sub-indicators and the composite indicator, represents the proportion of information from the input data retained in the composite indicator. Second, interpretability, measured by the number of Principal Components required to represent the multidimensional phenomenon, indicates the ease with which the phenomenon can be understood and interpreted. Third, explanatory power, assessed through the association between the composite indicator and an external variable conceptually related to the phenomenon, indicates its compatibility with the conceptual framework. In addition, the study develops an adaptive approach that seeks to reconcile interpretability, informational power, and conceptual consistency in representing social exclusion in Maringá, Paraná.