A Bayesian nonlinear mixed-effects location scale model for learning.

Area of Science:

• Psychometrics
• Statistical Modeling
• Cognitive Psychology

Background:

• Traditional statistical models often assume constant within-person variance, which may not accurately reflect learning processes.
• Understanding how individual means and variability change nonlinearly over time is crucial for cognitive research.

Purpose of the Study:

• To introduce and illustrate a novel Bayesian nonlinear mixed-effects location scale model (NL-MELSM).
• To enable the fitting of nonlinear trajectories to both the location (individual means) and scale (within-person variance) in longitudinal data.
• To explore the covariances between random effects for location and scale parameters, offering insights into the interplay of mean structure and variability.

Main Methods:

• Development of a Bayesian nonlinear mixed-effects location scale model (NL-MELSM).
• Incorporation of a sub-model for predicting nonlinear parameters for both location and scale.
• Estimation of random effects for all nonlinear parameters, drawn from a common multivariate distribution to capture covariances.

Main Results:

• The NL-MELSM successfully fits nonlinear functions to both the location and scale parameters.
• Estimation of covariances between random effects provides novel insights into the relationship between individual mean structures and intra-individual variability.
• Fitting a nonlinear function to within-person variance, with individual variation, significantly improved predictive accuracy compared to standard models.

Conclusions:

• The NL-MELSM offers a flexible and powerful approach for analyzing complex learning processes with nonlinear changes in means and variance.
• The model enhances predictive accuracy by accounting for individual differences in nonlinear trajectories of within-person variability.
• The Bayesian framework facilitates robust inference, model selection, and hypothesis testing for psychological research applications.