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Title: Covariate-modulated rectangular latent Markov models with an unknown number of regime profiles Authors:  Alfonso Russo - University of Rome Tor Vergata (Italy) [presenting]
Alessio Farcomeni - University of Rome Tor Vergata (Italy)
Maria Grazia Pittau - Sapienza - University of Rome (Italy)
Roberto Zelli - Sapienza - University of Rome (Italy)
Abstract: A multivariate latent Markov model with a number of latent states is derived that can possibly change at each time point. There are several applications in Macroeconomics, Microeconomics, Ecology or Epidemiology, where it might be desirable to allow for time-varying latent structures since new patterns might emerge or disappear over time, especially with multivariate outcomes. We give two main methodological contributions. First of all, we specify a completely general rectangular latent Markov model, where outcomes are a mix of continuous and categorical measurements and both the manifest and latent distributions are conditioned on covariates, which can be particularly useful to explain transitions across latent stages. Secondly, we derive an efficient transdimensional Markov Chain Monte Carlo sampler, to obtain the posterior distribution of all the parameters and for the sequence of a number of latent states. Bayesian inference is based on a Reversible Jump approach that is separately performed for each time occasion. In a simulation study, we show that our approach has a lower bias than competitors and that it can recover the true underlying sequence of latent states with high probability, even when covariates are omitted and independent of whether the true latent sequence varies with time or not. We conclude with an analysis of the well-being of 100 nations, as expressed by the dimensions of the Human Development Index, for six-time points spanning a period of 22 years.