Mixed effects state-space models with Student-t errors

In this article, mixed-effects state space models (MESSM, [Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485.]) are revisited. MESSM can be considered as an alternative to study the HIV dynamic in a longitudinal data environment, defining the mixed-effects component into state-space models setup. As in Liu et al.[Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485.], we consider a hierarchical structure to capture possible differences between the immune systems for different patients. We extend MESSM, allowing observational errors to follow a more flexible distribution to take account for heavy tails. Using the Bayesian paradigm, an efficient Markov Chain Monte Carlo (MCMC) algorithm based on McCausland et al. [McCausland WJ, Miller S, Pelletier D. Simulation smoothing for state.space models: A computational efficiency analysis. Comput Stat Data Anal. 2011;55(1):199–212.] is introduced for parameter and latent variables estimation. Moreover, the mixing variables obtained as a by-product of the scale mixture representation can be used to identify outliers. The methodology is illustrated using artificial and real datasets in order to investigate the properties and performance of the proposed model.