1.Department of Business and Economics, University of Cagliari, Viale S. Ignazio 17, 09123, Cagliari, Italy ;2.Department of Statistical Sciences, Catholic University of Milan, Largo Gemelli 1, 20123, Milan, Italy ;
Abstract:
A novel criterion for estimating a latent partition of the observed groups based on the output of a hierarchical model is presented. It is based on a loss function combining the Gini income inequality ratio and the predictability index of Goodman and Kruskal in order to achieve maximum heterogeneity of random effects across groups and maximum homogeneity of predicted probabilities inside estimated clusters. The index is compared with alternative approaches in a simulation study and applied in a case study concerning the role of hospital level variables in deciding for a cesarean section.