Random effects clustering in multilevel modeling: choosing a proper partition

A novel criterion for estimating a latent partition of the observed groups based on the\r\noutput of a hierarchical model is presented. It is based on a loss function combining\r\nthe Gini income inequality ratio and the predictability index of Goodman and Kruskal\r\nin order to achieve maximum heterogeneity of random effects across groups and\r\nmaximum homogeneity of predicted probabilities inside estimated clusters. The index\r\nis compared with alternative approaches in a simulation study and applied in a case\r\nstudy concerning the role of hospital level variables in deciding for a cesarean section.