Regularized Continuous Time Structural Equation Models: A Network Perspective.

Regularized continuous time structural equationmodels 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. In recent years, the complexity of longitudinal study designs and data analytic approaches has increased tremendously. For example, inmodern panel designswithmany individuals but fewmeasurement occasions, people are often observed at very different points in time, resulting in a complex pattern of (missing) data. Likewise, in single subject time series, measurement occasions are usually not equidistantly spaced, which violates a standard assumption of many statistical models. However, not only study designs becamemore complex but also the statistical models that are being used for data analyses. Network models, for example, can easily contain dozens or hundreds of parameters. Such complex models might provide valuable insights into the dynamics of psychological processes, but they are also difficult to interpret and prone to overfitting. In this article, we introduce regularized continuous time structural equation modeling (regularized CTSEM) as a solution to both problems. By adopting a CTSEM approach, we resolve the problem of unequally spaced measurement occasions in dynamic modeling. By adopting different types of LASSO regularization, we simplify model interpretation and prevent overfitting. Our approach is implemented in the R (R Core Team, 2022) package regCtsem. We demonstrate the use of regCtsem in a simulation study that shows that in particular in small sample sizes regCtsem improves the parameter estimates. Furthermore, two empirical examples are presented: A panel data example and a time series example. We end with a discussion on current limitations and future research directions. [ABSTRACT FROM AUTHOR]