Covariate-modulated rectangular latent Markov models with an unknown number of regime profiles

We derive a multivariate latent Markov model with number of latent states that can possibly change at each time point. We model both the manifest and latent distributions conditionally on explanatory variables. Bayesian inference is based on a transdimensional Markov Chain Monte Carlo approach, where Reversible Jump is separately performed for each time occasion. In a simulation study, we show how our approach can recover the true underlying sequence of latent states with high probability, and that it has lower bias than competitors. 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. R code with an implementation is available as supplementary material, together with files for reproducing the data analysis.