Mixed hidden Markov models for quantiles

We propose a mixed hidden Markov model for continuous longitudinal data, to the quantile regression perspective. Time-constant and time-varying random parameters are added in the quantile regression model to account for time-invariant and dynamic unobserved factors affecting the variable of interest. A nonparametric maximum likelihood approach is applied to solve the numerical integration problem typically arising in the mixed model framework. Parameter estimates are then obtained by means of an EM algorithm, easily derived by exploiting the forward and backward variables defined in the so called Baum-Welsh recursion.