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Fitting growth curve models in the Bayesian framework.

Zita Oravecz1, Chelsea Muth2

  • 1The Pennsylvania State University, 216 Health and Human Development Building, State College, PA, USA. zita@psu.edu.

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Summary

This paper introduces fitting growth curve models using the hierarchical Bayesian framework. It provides practical guidelines and computer scripts for analyzing longitudinal data, enhancing understanding of within-person and between-person changes.

Keywords:
Bayesian modelingGrowth curve modeling

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Area of Science:

  • Methodology in Social Sciences
  • Statistical Modeling
  • Longitudinal Data Analysis

Background:

  • Growth curve models (GCMs) are versatile for analyzing within-person and between-person effects over time.
  • Existing methods may lack flexibility for complex longitudinal data structures.
  • Bayesian approaches offer a robust framework for parameter estimation and uncertainty quantification.

Purpose of the Study:

  • To provide a practical guide for fitting growth curve models within a hierarchical Bayesian framework.
  • To demonstrate the application of Bayesian GCMs using real-world longitudinal data.
  • To equip researchers with the necessary tools and code for implementing these models.

Main Methods:

  • Mathematical formulation of growth curve models.
  • Step-by-step guidelines for fitting models in a hierarchical Bayesian framework.
  • Implementation using JAGS and R statistical software, including provided scripts and data.

Main Results:

  • Successful application of the Bayesian GCM approach to a longitudinal marital relationship quality dataset.
  • Demonstration of how to analyze both individual change trajectories and group-level differences.
  • Code and data are provided for reproducible research and hands-on learning.

Conclusions:

  • The hierarchical Bayesian framework offers a powerful and flexible approach to growth curve modeling.
  • This paper facilitates the adoption of Bayesian GCMs for researchers analyzing longitudinal data.
  • Practical implementation guidance and reproducible code enhance the accessibility of advanced statistical methods.