Utility of a slopes difference test for probing longitudinal multilevel aptitude treatment interactions: a simulation

Area of Science:

• Educational Psychology
• Quantitative Psychology
• Statistical Modeling

Background:

• Precision education aims to tailor interventions to individual student needs.
• Aptitude-treatment interactions (ATI) and skill-by-treatment interactions (STI) are key frameworks for understanding differential intervention effects.
• Longitudinal multilevel modeling is a suitable statistical approach for analyzing such interactions over time.

Purpose of the Study:

• To investigate the statistical power of slopes difference tests within longitudinal multilevel models.
• To identify crucial design factors influencing the power and reliability of these tests.
• To compare the power of slopes difference tests in longitudinal multilevel modeling versus traditional multiple regression.

Main Methods:

• A simulation study was employed to assess statistical power.
• Key design factors manipulated included effect size, number of data collection waves, number of clusters, participants per cluster, treatment assignment proportion, and intraclass correlation.
• Slopes difference tests were examined within a longitudinal multilevel modeling framework.

Main Results:

• Effect size, number of waves, number of clusters, and participants per cluster were identified as the most significant determinants of statistical power.
• These factors also strongly influenced model convergence and rates of singularity.
• Slopes difference tests demonstrated higher power in longitudinal multilevel modeling compared to their application in multiple regression.

Conclusions:

• The findings provide critical insights into the power of slopes difference tests for detecting ATI/STI in longitudinal educational research.
• Researchers can optimize study designs by considering the identified influential factors to enhance statistical power and model stability.
• The study supports the utility of slopes difference tests within longitudinal multilevel modeling for advancing precision education.