Modeling Cycles, Trends and Time-Varying Effects in Dynamic Structural Equation Models with Regression Splines

Area of Science:

• Quantitative Psychology
• Statistical Modeling
• Longitudinal Data Analysis

Background:

• Intensive longitudinal data (ILD) are increasingly common, enabling advanced analyses beyond traditional growth models.
• Dynamic structural equation models (DSEMs) are popular for ILD but struggle with unspecified nonlinear effects.
• Accurately modeling trends, cycles, and time-varying predictors in DSEMs remains a practical challenge.

Purpose of the Study:

• To introduce regression splines as a flexible tool for DSEM to model nonlinear effects in ILD.
• To provide a building block for DSEM modelers to handle complex functional shapes.
• To demonstrate the application of smoothing priors and hierarchical smooth terms within DSEMs.

Main Methods:

• Integration of regression splines into the DSEM framework to flexibly learn underlying function shapes.
• Application of smoothing priors and hierarchical smooth terms for modeling complex temporal dependencies.
• Simulation studies to evaluate the impact of ignoring nonlinear trends on parameter estimates.

Main Results:

• Ignoring nonlinear trends in DSEMs can lead to biased parameter estimates.
• Regression splines effectively capture nonlinear patterns, such as weekly cycles and long-term trends.
• The proposed framework successfully models complex temporal dynamics in diary data.

Conclusions:

• Regression splines offer a powerful and flexible extension to DSEMs for analyzing ILD with nonlinear effects.
• This approach enhances the DSEM toolkit, allowing for more accurate modeling of trends and cycles.
• The method is applicable to real-world diary data, improving the understanding of alcohol consumption and stress dynamics.