Moon-Ho Ho, Robert Shumway, and Hernando Ombao
Ho, Shumway and Ombao present a self-contained treatment of state space modeling and try to make the exposition accessible to those who have relatively little prior knowledge of the subject. They focus on issues of modeling and show how state space models offer rich and flexible class of structures that accommodate both the static and dynamic nature of intensive longitudinal data. Longitudinal data collected from a group or groups of subjects following over time often exhibits within-subject serial correlations, involve random subject effects, and presence of observational errors. Researchers are usually interested in describing the trend over time, whether there are significant differences in the trend across groups of subjects and what factors can account for this trend and differences. Longitudinal data presents opportunities for exploiting state space methods for multivariate longitudinal models that can be expressed in state space form. Such representation opens new opportunities for modeling intensive longitudinal data by extending the usual mixed model to allow dynamic random effects and time-varying covariates with stochastic coefficients in parametric or nonparametric manner, and estimate long-term and short-term covariate effects. Furthermore, state space models provide convenient methodology for treating incomplete and unequally spaced data. Parameters in the state space models are estimated through the use of Kalman filter and smoother. When used in conjunction with the Expectation-Maximization (EM) algorithm, they offer an elegant approach to handling incompletely observed multivariate vectors. The computational burden is much less in state space models than the usual mixed models. The authors illustrate the application of state space models in nonstandard situations for analyzing intensive longitudinal data collected in neuroscientific and traffic network studies. The use of state space models in social sciences except economics is not common. Through the two case studies presented in this chapter, the authors hope the readers will be convinced that state space models provide an effective means for practical analysis of intensive longitudinal data and will consider the use of state space models in their own work.