Testing for Within × Within and Between × Within Moderation using Random Intercept Cross-Lagged Panel Models

Area of Science:

• Developmental Psychology
• Quantitative Psychology
• Psychopathology Research

Background:

• Random-Intercept Cross-Lagged Panel Models (RI-CLPMs) are increasingly used to study developmental processes.
• These models effectively decompose individual measurements into stable between-person and fluctuating within-person components.
• However, implementing and interpreting interaction effects within RI-CLPMs presents unique challenges for researchers.

Purpose of the Study:

• To provide a clear guide for developmental researchers on implementing, testing, and interpreting interaction effects in RI-CLPMs.
• To illustrate the analysis of specific interaction types: Within × Within and Between × Within.
• To demonstrate these methods using a real-world dataset and a Bayesian Structural Equation Modelling framework.

Main Methods:

• Utilized data from the Millennium Cohort Study, a UK-based longitudinal dataset.
• Employed a Bayesian Structural Equation Modelling (SEM) framework for advanced statistical analysis.
• Provided annotated Mplus code to facilitate the practical application of the described methods.

Main Results:

• Successfully demonstrated the implementation and interpretation of Within × Within interactions.
• Successfully demonstrated the implementation and interpretation of Between × Within interactions.
• Showcased how to disentangle complex within-person and between-person dynamics over time.

Conclusions:

• RI-CLPMs offer a powerful approach for dissecting developmental dynamics.
• The methods described allow for a nuanced understanding of interaction effects in developmental research.
• The provided code and framework enable researchers to confidently analyze complex longitudinal data.