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SEM Based CARMA Time Series Modeling for Arbitrary N.

Johan H L Oud1, Manuel C Voelkle2, Charles C Driver3

  • 1a Behavioural Science Institute , Radboud University , Nijmegen , The Netherlands.

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|November 8, 2017
PubMed
Summary
This summary is machine-generated.

This study details continuous-time autoregressive moving-average (CARMA) models within structural equation modeling (SEM). The methods are demonstrated for single-subject and group data, offering robust statistical analysis for time-series data.

Keywords:
CARMA modelsContinuous timeN = 1-researchinterindividual and intraindividual researchstate space modelingstructural equation modelingtime series

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Area of Science:

  • Psychometrics
  • Quantitative Psychology
  • Time Series Analysis

Background:

  • Structural equation modeling (SEM) is a powerful tool for analyzing complex relationships.
  • Continuous-time models offer advantages for irregularly timed or densely sampled longitudinal data.
  • Existing methods often focus on aggregate-level analysis, limiting insights into individual-level dynamics.

Purpose of the Study:

  • To present a detailed framework for state-space specification and estimation of continuous-time autoregressive moving-average (CARMA) models.
  • To extend these methods to both single-subject (N=1) and multi-subject (N>1) analyses within an SEM context.
  • To introduce a subject-group-reproducibility test for comparing aggregate and individual models.

Main Methods:

  • State-space modeling of first and higher-order CARMA processes.
  • Estimation within an extended SEM framework using the ctsem R-package.
  • Simulations with varying sample sizes (N=1,000, N=100, N=50) and time points (T=41).
  • Application of a subject-group-reproducibility test.
  • Empirical example analyzing mood dynamics in N=55 women.

Main Results:

  • The proposed state-space approach effectively estimates CARMA models for both N=1 and N>1 data.
  • Simulations demonstrate the feasibility and accuracy of the method across different sample sizes.
  • The subject-group-reproducibility test provides a reliable way to assess model consistency.
  • The empirical example successfully illustrates the application to real-world mood dynamics.

Conclusions:

  • The ctsem R-package provides a flexible and powerful tool for advanced longitudinal data analysis.
  • The state-space framework for CARMA models enhances the ability to model complex temporal processes at both individual and group levels.
  • This approach offers significant advancements for researchers studying dynamic systems in psychology and related fields.