Constrained optimization for addressing spatial heterogeneity in principal component analysis: an application to composite indicators

Principal component analysis, in its standard version, might not be appropriate for the analysis of spatial data. Particularly, the presence of spatial heterogeneity has been recognized as a possible source of misspecification for the derivation of com- posite indicators using principal component analysis. In recent times, geographically weighted approach to principal component analysis has been used for the treatment of continuous heterogeneity. However, this technique poses problems for the treat- ment of discrete heterogeneity and the interpretation of the results. The aim of this paper is to present a new approach to consider spatial heterogeneity in principal component analysis by using simulated annealing algorithm. The proposed method is applied for the definition of a composite indicator of local services for 121 munic- ipalities in the province of Rome.