Regularized Continuous Time Structural Equation Models: A Network Perspective

Regularized continuous time structural equation models are proposed to address two recent challenges in longitudinal research: Unequally spaced measurement occasions and high model complexity. Unequally spaced measurement occasions are part of most longitudinal studies, sometimes intentionally (e.g., in experience sampling methods) sometimes unintentionally (e.g., due to missing data). Yet, prominent dynamic models, such as the autoregressive cross-lagged model, assume equally spaced measurement occasions. If this assumption is violated parameter estimates can be biased, potentially leading to false conclusions. Continuous time structural equation models (CTSEM) resolve this problem by taking the exact time point of a measurement into account. This allows for any arbitrary measurement scheme. We combine CTSEM with LASSO and adaptive LASSO regularization. Such regularization techniques are especially promising for the increasingly complex models in psychological research, the most prominent example being network models with often dozens or hundreds of parameters. Here, LASSO regularization can reduce the risk of overfitting and simplify the model interpretation. In this article we highlight unique challenges in regularizing continuous time dynamic models, such as standardization or the optimization of the objective function, and offer different solutions. Our approach is implemented in the R (R Core Team, 2022) package regCtsem. We demonstrate the use of regCtsem in a simulation study, showing that the proposed regularization improves the parameter estimates, especially in small samples. The approach correctly eliminates true-zero parameters while retaining true-nonzero parameters. We present two empirical examples and end with a discussion on current limitations and future research directions.