Latent drop-out hidden Markov model with mixed effects

We propose a class of models for the analysis of longitudinal data subject to non-ignorable drop-out. A mixed hidden Markov model for the longitudinal process is introduced with a latent drop-out class describing the influence of missingness on the response variable. A conditional generalized linear model is specified for the longitudinal profile to express dependence between observations from the same individual due to time-constant and time-varying latent characteristics. Furthermore, a latent drop-out variable is considered to explain differences between individuals having different drop-out patterns. The probability of being in one of the drop-out class is modelled through an ordinal logit model, including the time to drop-out as covariate. Parameter estimates are obtained via an EM algorithm to take into account of the presence of several (discrete and continuous) latent variables.