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

Ø Sørensen1, E M McCormick2

  • 1Department of Psychology, Center for Lifespan Changes in Brain and Cognition, University of Oslo, Oslo, Norway.

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Summary
This summary is machine-generated.

This study introduces regression splines to dynamic structural equation models (DSEMs) for analyzing intensive longitudinal data. This flexible approach accurately captures nonlinear trends and cycles, improving parameter estimation in complex data.

Keywords:
DSEMStanintensive longitudinal dataregression splinessmoothing

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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.