Representing Multidimensional Phenomena of Geographic Interest: Benefit of the Doubt or Principal Component Analysis?

Abstract

Composite indicators are one-dimensional measures of multidimensional phenomena. Through the composite indicators, it is possible to have a single map of the different subindicators of poverty, inequality, sustainability, and economic development. This research employs two well-known methods of building composite indicators to represent the social exclusion of eight cities. This research shows that the benefit of the doubt and principal component analysis have limitations to representing multidimensional phenomena of geographic interest, but adaptations in these methods reduce these limitations. The benefit of the doubt constrained (BoD-c) restricts subindicator weight variations, increasing the composite indicator’s capacity to represent the most important subindicator in the concept of the multidimensional phenomenon. The principal component analysis adjusted (PCA-a) discards poorly correlated subindicators, ensuring a variance extracted in the first component above the acceptance threshold of 0.50. Contrasting BoD-c and PCA-a, geographically weighted principal component analysis has a limited capacity to capture the most important subindicator in the concept of the multidimensional phenomenon. Among twenty-three experts from nine countries, eighteen preferred PCA-a to BoD-c, indicating that information loss is not as critical a property as full comparability across geographic areas. Local experts agree that both maps represent local social reality, but PCA-a is more faithful to that reality.