Representing social exclusion in geographic space: interpretability or informational power?

Social exclusion is a complex, multidimensional phenomenon, and its understanding requires simultaneously considering economic, educational, household, and environmental aspects. In this context, composite indicators facilitate understanding social exclusion by simultaneously considering its multiple aspects through a one-dimensional measure. Composite indicators can be constructed using numerous methods, including Principal Component Analysis, one of the most popular. However, the method has limitations, such as information loss and interpretability. Information loss can be substantial when the multidimensional phenomenon aspects are poorly intercorrelated. In this situation, numerous Principal Components must be considered simultaneously to understand the multidimensional phenomenon, rekindling the interpretability problem that composite indicators pursue to solve. This study develops a novel approach that balances information power and interpretability in composite indicators constructed by Principal Component Analysis. The study reveals that information loss is not influenced solely by low intercorrelation but by information diversity and correlation with a conceptually significant indicator. These findings indicate that disregarding poorly intercorrelated aspects that transfer low information to the composite indicator does not diminish its conceptual scope but ensures greater information power and interpretability. In particular, the developed approach effectively captured the concept of social exclusion with satisfactory information power in the first Principal Component. Principal Component Analysis and Geographically Weighted Principal Component Analysis need three Principal Components to achieve satisfactory information power, compromising the social exclusion interpretability. The study findings point to the relevance of adopting a new practice of constructing composite indicators through Principal Component Analysis in which interpretability and informational power are balanced.