Bayesian modeling of associations in bivariate piecewise linear mixed-effects models

Area of Science:

• Statistics
• Developmental Psychology
• Educational Measurement

Background:

• Longitudinal processes often involve interdependent growth curves that change in non-constant patterns across developmental segments.
• Existing bivariate piecewise mixed-effects models have limitations, including uncorrelated residual errors and restricted random-effects modeling.

Purpose of the Study:

• To develop a Bayesian bivariate piecewise linear mixed-effects model (BPLMEM) for simultaneously modeling two segmented longitudinal processes.
• To estimate the association between error variances and provide a robust framework for joint random-effects modeling.
• To address limitations in prior bivariate piecewise mixed-effects models.

Main Methods:

• Developed a Bayesian bivariate piecewise linear mixed-effects model (BPLMEM).
• Investigated model performance using a Monte Carlo simulation study.
• Applied the BPLMEM to the Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K) dataset.

Main Results:

• The developed BPLMEM provides a more robust modeling choice for joint random-effects and error variance associations.
• The model successfully examined the joint development of mathematics and reading achievement scores in the ECLS-K data.
• New insights into the longitudinal association between mathematics and reading trajectories were obtained.

Conclusions:

• The Bayesian BPLMEM offers a flexible and robust statistical framework for analyzing interdependent, segmented longitudinal data.
• The model enhances the understanding of complex developmental relationships, such as those between academic skills.
• This approach advances the analysis of joint developmental trajectories in educational and psychological research.