A 3-level Bayesian mixed effects location scale model with an application to ecological momentary assessment data.

Area of Science:

• Psychometrics and Statistical Modeling
• Longitudinal Data Analysis
• Behavioral Science

Background:

• Ecological momentary assessment (EMA) generates intensive longitudinal data, often requiring advanced statistical methods to analyze changes in mean and variance.
• Existing 2-level and 3-level location scale models have limitations in capturing wave-specific heterogeneity in variance.
• There is a need for a more comprehensive model to address complex data structures in EMA, particularly accounting for subject heterogeneity across multiple waves.

Purpose of the Study:

• To propose a novel 3-level location scale model for EMA data with observations nested within waves and waves nested within subjects.
• To account for subject heterogeneity at baseline and across different waves in both the mean and variance of responses.
• To provide a flexible framework for analyzing changes in psychological states and their variability over time in longitudinal studies.

Main Methods:

• Development of a comprehensive 3-level location scale model accommodating nested data structures (observations within waves, waves within subjects).
• Implementation of Bayesian estimation using Markov Chain Monte Carlo (MCMC) methods via Stan statistical software.
• Validation through simulation studies and application to an adolescent smoking EMA dataset.

Main Results:

• The proposed 3-level location scale model demonstrated superior fit compared to existing models.
• Significant subject heterogeneity was identified at baseline and across waves for both mood mean and variance.
• The model successfully captured dynamic changes in response variability over time.

Conclusions:

• The developed 3-level location scale model offers a powerful tool for analyzing complex EMA data, revealing nuanced patterns of psychological variability.
• This approach enhances understanding of individual differences and temporal dynamics in mood and behavior, applicable across various research fields.
• The findings underscore the importance of considering wave-specific heterogeneity in variance for accurate interpretation of longitudinal psychological data.