A comparison of some criteria for states selection in the latent Markov model for longitudinal data

摘要

We compare different selection criteria to choose the number of latent statesof a multivariate latent Markov model for longitudinal data. This model isbased on an underlying Markov chain to represent the evolution of a latentcharacteristic of a group of individuals over time. Then, the responsevariables observed at the different occasions are assumed to be conditionallyindependent given this chain. Maximum likelihood of the model is carried outthrough an Expectation-Maximization algorithm based on forward-backwardrecursions which are well known in the hidden Markov literature for timeseries. The selection criteria we consider in our comparison are based onpenalized versions of the maximum log-likelihood or on the posteriorprobabilities of belonging to each latent state, that is the conditionalprobability of the latent state given the observed data. A Monte Carlosimulation study shows that the indices referred to the log-likelihood basedinformation criteria perform in general better with respect to those referredto the classification based criteria. This is due to the fact that the lattertend to underestimate the true number of latent states, especially in theunivariate case.