Estimating multivariate longitudinal trajectories using mixed-effects models with crossed random effects

Area of Science:

• Statistics
• Longitudinal Data Analysis
• Developmental Psychology

Background:

• Cohort-sequential designs often involve planned missing data, complicating longitudinal trajectory analysis.
• Estimating within- and between-variability in multivariate trajectories requires robust statistical methods.
• Continuous-time metrics are typically needed for complex longitudinal designs.

Purpose of the Study:

• To evaluate a mixed-effects model with crossed random effects for estimating variability in longitudinal multivariate trajectories.
• To assess the model's performance in cohort-sequential designs with planned missing data.
• To demonstrate the model's utility for forecasting individual and variable-specific trajectories.

Main Methods:

• Simulations were conducted to evaluate model outcomes under varying cluster sizes and trajectory complexities.
• A mixed-effects model with crossed random effects for individuals and variables was employed.
• An empirical illustration using cognitive developmental data was used for validation.

Main Results:

• The model successfully estimates general and variable-specific trajectories and their variability.
• Standard errors for random effects were wide but crucial for substantive variable-specific decisions.
• Model predictions accurately forecast complete individual and variable-specific trajectories from limited observations.

Conclusions:

• The proposed mixed-effects model provides a promising and accessible tool for multivariate longitudinal data analysis.
• Researchers can reconstruct complete individual trajectories for multiple variables across a target age range.
• The model's simplicity makes it a valuable alternative to more complex analytical approaches.