Gaussian Process Panel Modeling – Kernel-Based Longitudinal Modeling

Longitudinal panel data obtained from multiple individuals measured at multiple time points are crucial for psychological research. To analyze such data, a variety of modeling approaches such as hierarchical linear modeling or linear structural equation modeling are available. Such traditional parametric approaches are based on a relatively strong set of assumptions, which are often not met in practice. We present a flexible modeling approach for longitudinal data that is based on the Bayesian statistical learning method Gaussian Process Regression. We term this novel approach Gaussian Process Panel Modeling (GPPM). We show that GPPM subsumes most common modeling approaches for longitudinal data such as linear structural equation models and state-space models as special cases but also extends the space of expressible models beyond them. GPPM offers great flexibility in model specification, facilitates both parametric and nonparametric modeling in a single framework, enables continuous-time modeling as well as person-specific predictions, and offers a modular system that allows the user to piece together hypotheses about change by selecting from and combining predefined types of trajectories or dynamics. We demonstrate the utility of GPPM based on a selection of models and data sets.