Functional Modeling of Longitudinal Data with the SSM Procedure

In many studies, a continuous response variable is repeatedly measured over time on one or more subjects. The subjects might be grouped into different categories, such as cases and controls. The study of resulting observation profiles as functions of time is called functional data analysis. This paper shows how you can use the SSM procedure in SAS/ETS® software to model these functional data by using structural state space models (SSMs). A structural SSM decomposes a subject profile into latent components such as the group mean curve, the subject-specific deviation curve, and the covariate effects. The SSM procedure enables you to fit a rich class of structural SSMs, which permit latent components that have a wide variety of patterns. For example, the latent components can be different types of smoothing splines, including polynomial smoothing splines of any order and all L-splines up to order 2. The SSM procedure efficiently computes the restricted maximum likelihood (REML) estimates of the model parameters and the best linear unbiased predictors (BLUPs) of the latent components (and their derivatives). The paper presents several real-life examples that show how you can fit, diagnose, and select structural SSMs; test hypotheses about the latent components in the model; and interpolate and extrapolate these latent components.