Harnessing Spatial Heterogeneity in Composite Indicators through the Ordered Geographically Weighted Averaging (OGWA) Operator

Spatially heterogeneous weights and a non-compensatory aggregation scheme, are two important properties needed to construct a composite indicator capable of summarizing properly the multidimensional phenomenon of local spatial units. Such a composite indicator takes into account, on the one hand, the latent characteristics of the specific units related to their location in the territory, and on the other hand, the relative importance of sub-indicators highlighting both positive and negative aspects of the studied phenomena. Under these premises, this article proposes a new method called Ordered Geographically Weighted Averaging (OGWA), which can consider different degrees of non-compensability between sub-indicators and, at the same time, the spatial heterogeneity for continuous, ordinal, and mixed data. The properties of the method are evaluated through a simulation study. Finally, the method is applied to construct a composite indicator to map the urban public infrastructure of Sao Sebastiao do Paraiso, a city located in the southeastern region of Brazil.