Computational procedures for quality assessment of latent concepts

The estimation of a latent construct is a crucial issue when a phenomenon is a consequence of the joint occurrence of multiple features. Several techniques for estimating latent phenomena are proposed in literature, but since the variable under study is unobservable, and the law by which the features combine together is unknown, comparison of results obtained with different methods is achieved through simulationbased analyses. The latent construct is measured by a multidimensional index (MI), which determines a ranking among the observations. It is therefore relevant to assess the reliability of the methods by which such rankings are produced. In this paper, we propose two procedures evaluating the assessment of latent constructs and the corresponding rankings. The first one is a simulation-based mean square error, which evaluates the MI accuracy, while the second one uses a simulation average split ranking index, which assesses its reliability. Both methodologies are illustrated with an application to the assessment of the urban sustainability, and three methodologies of building MIs are compared: the first one based on structural equation models; the second one based on principal component analysis; and the third one that uses an equal weight method.