Title: Time-specific clustering via rectangular latent Markov models, with an analysis of the well-being of nations
Authors: Alessio Farcomeni - Sapienza - University of Rome (Italy) [presenting]
Gordon Anderson - University of Toronto (Canada)
Maria Grazia Pittau - Sapienza - University of Rome (Italy)
Roberto Zelli - Sapienza - University of Rome (Italy)
Abstract: In longitudinal model-based clustering methods the number of groups is usually fixed over time, apart from (mostly) heuristic approaches. We propose a latent Markov model admitting variation in the number of latent states. The consequence is that (i) subjects can switch from one group to another at each time period and (ii) the number of groups can change at each time period. Clusters can merge, split, or be re-arranged. For a fixed sequence of the number of groups, inference is carried out through maximum likelihood, using appropriate forward-backward recursions. A penalized likelihood form is introduced to simultaneously choose an optimal sequence for the number of groups and cluster subjects. The penalized likelihood is optimized through a novel expectation-maximization-Markov-Metropolis algorithm. The motivation arises from an analysis of the progress of well-being of nations, as measured by the three dimensions of the Human Development Index over the last 25 years. The main findings are that (i) transitions among nation clubs are scarce, and mostly linked to historical events (like dissolution of USSR or war in Syria) and (ii) there is mild evidence that the number of clubs has shrunk over time, where we have four clusters before 2005 and three afterwards. In a sense, nations are getting more and more polarized with respect to standards of well-being. R code is available at https://github.com/afarcome/LMrectangular.