Assessing environmental quality by clustering a structural equation model based index

This paper proposes an innovative computational procedure to determine the optimal number of clusters. The aim is to identify the maximum number of significantly distinct clusters, when the centroids are orderable and order is relevant. The insight is that ranking according to this optimal number of clusters allows to better classify units in order to assess their quality with regard to a variable of interest. By means of bootstrap confidence intervals estimated on clusters’ centroids, the procedure allows to identify the optimal number of “well-separated” groups. The centroids are obtained applying a unidimensional k-means clustering and they allow to classify and rank the measure of an Index based on a Structural Equation Model. The procedure ranks European cities according to their level of air pollution.