Structured Flexibility: Gaussian Process Regression as a Complement to Linear Models in Political Science

Political scientists routinely face uncertainty about functional forms when modeling relationships in their data, balancing flexibility with theoretical structure and interpretability. We introduce Gaussian process regression (GPR) as a valuable complement to existing methods that uniquely combines these features. GPR places priors directly on functions rather than parameters, allowing researchers to encode theoretical knowledge where it exists while remaining agnostic about functional forms where theory is uncertain. This modular framework naturally extends familiar linear models to accommodate complex patterns while providing full posterior distributions for quantities of interest. We demonstrate GPR’s versatility through three applications of increasing complexity: analyzing social media trends around critical events, modeling individual-level trajectories with common shocks, and estimating treatment effects in panel data with unit-specific patterns. Using GPyTorch, we provide practical guidance for implementation that enables both exact estimation in small samples and efficient approximate inference for larger datasets.

2026