Modeling individual differences in the timing of change onset and offset

Area of Science:

• Multidisciplinary research
• Longitudinal data analysis
• Developmental psychology

Background:

• Longitudinal studies often examine individual differences in developmental timing.
• Existing statistical models struggle to directly estimate the timing of developmental changes.
• The time-to-criterion framework has limitations when criterion values vary or are unknown.

Purpose of the Study:

• To develop a flexible statistical framework for modeling individual differences in the timing of developmental change.
• To extend existing models to accommodate onset, offset, and S-shaped trajectories.
• To provide a method for analyzing when developmental processes start, stop, or change pace.

Main Methods:

• Combines reparameterized quadratic and multiphase models.
• Models decelerating change to an offset point (maximum or minimum).
• Models accelerating change from an onset point and S-shaped curves with both onset and offset.

Main Results:

• The proposed model allows for individual differences in the timing of change (onset and offset) and ultimate outcome levels.
• Demonstrates applicability to inverted J-shaped, J-shaped, and S-shaped trajectories.
• Successfully applied across neuroscience, educational psychology, developmental psychology, and cognitive science.

Conclusions:

• The developed modeling framework accurately captures individual differences in the timing of developmental change.
• This approach offers a significant advancement for analyzing complex developmental trajectories in longitudinal research.
• The model's flexibility makes it broadly applicable to diverse scientific domains investigating change over time.