A hidden Markov model for variable selection with missing values

We propose a hidden Markov model for longitudinal multivariate continuous responses, accounting for missing data under the missing at random assumption. Maximum likelihood estimation of this model is carried out through the Expectation-Maximization algorithm. To address the problem of dimensionality reduction, we develop a greedy search algorithm based on the Bayesian Information Criterion. We illustrate the proposal through a dataset collected by the World Bank and UNESCO Institute for Statistics on the basis of which we dynamically cluster countries according to the selected variables observed during the period 2000-2017.