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Updated: Jul 5, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Identifiability and estimability of Bayesian linear and nonlinear crossed random effects models.
Corissa T Rohloff1, Nidhi Kohli1, Eric F Lock2
1Quantitative Methods in Education, Department of Educational Psychology, University of Minnesota, Minneapolis, Minnesota, USA.
This study introduces a Bayesian piecewise crossed random effects model (CREM) for nonlinear growth. Sufficient repeated measurements are crucial for accurately estimating group effects in longitudinal data analysis.
Area of Science:
- Statistics
- Biostatistics
- Longitudinal Data Analysis
Background:
- Crossed random effects models (CREMs) are vital for longitudinal data with dynamic group membership.
- Existing CREMs cannot model intrinsically nonlinear growth.
- Data conditions for identifying longitudinal CREMs, especially group effects, are unknown.
Purpose of the Study:
- Develop a Bayesian piecewise CREM for intrinsically nonlinear growth.
- Evaluate data conditions for identifying linear and nonlinear longitudinal CREMs.
- Assess the impact of functional form complexity on data requirements.
Main Methods:
- Developed a Bayesian piecewise crossed random effects model (CREM).
- Conducted three simulation studies to assess identification conditions.
- Applied the piecewise CREM to real-world longitudinal data.
Main Results:
- The number of repeated measurements per group significantly impacts group effect recovery.
- Increased functional form complexity necessitates more data for accurate estimation.
- Identified key data conditions for estimating linear, quadratic, and piecewise CREMs.
Conclusions:
- The developed Bayesian piecewise CREM effectively models nonlinear longitudinal growth.
- Data collection strategies must consider the number of repeated measurements and model complexity.
- Findings provide essential guidance for applying CREMs to longitudinal data.
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