Examining the feasibility of quadratic vector autoregressions for psychological intensive longitudinal data

What the paper says

• Nonlinear dynamical relationships among psychological variables can give rise to complex phenomena; however, methods to model these nonlinear relationships remain sparse. • We introduce a quadratic vector autoregression model applicable to psychological intensive longitudinal data and evaluate its performance. • Modeling nonlinear relationships poses unique challenges, but such methods are valuable for exploring potential nonlinear dynamics in data. Nonlinear relationships among variables play an important role in psychological modeling and understanding changes over time from intensive longitudinal data (ILD). Most methods focus on linear relationships, with a few exceptions developed for specific nonlinear interactions or general system dynamics. Methods considering multiple possible nonlinear relationships among all variables remain rare, hindered by challenges like overfitting and interpretation difficulties. This article examines the feasibility of applying a quadratic vector autoregression method to psychological ILD, using the Regularization Algorithm under Marginality Principle (RAMP) alongside a local linearization method for interpretation. We evaluated its performance with simulated and empirical datasets using classification metrics, information criteria, and cross-validation. Results show this method often requires a long time series for satisfactory performance. While information criteria favor the quadratic model in empirical datasets, cross-validation favors simpler AR models. Nonetheless, these two challenges are comparable to those in idiographic linear VAR models. Clear evidence of nonlinear relationships among variables supports the value of this method for exploratory studies. We developed an R package, quadVAR, as an implementation of this method.