Estimating mixed-effects state-space models via particle filters and the EM algorithm

In this paper, we focus on studying the Mixed-Effects State-Space (MESS) models previously introduced by 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 propose an estimation method by combining the auxiliary particle learning and smoothing approach with the Expectation Maximization (EM) algorithm. First, we describe the technical details of the algorithm steps. Then, we evaluate their effectiveness and goodness of fit through a simulation study. Our method requires expressing the posterior distribution for the random effects using a sufficient statistic that can be updated recursively, thus enabling its application to various model formulations including non-Gaussian and nonlinear cases. Finally, we demonstrate the usefulness of our method and its capability to handle the missing data problem through an application to a real dataset.