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

Abstract

Random-Intercept Cross-Lagged Panel Models allow for the decomposition of measurements into between- and within-person components and have hence become popular for testing developmental hypotheses. Here, we describe how developmental researchers can implement, test and interpret interaction effects in such models using an empirical example from developmental psychopathology research. We illustrate the analysis of Within × Within and Between × Within interactions utilising data from the United Kingdom-based Millennium Cohort Study within a Bayesian Structural Equation Modelling framework. We provide annotated Mplus code, allowing users to isolate, estimate and interpret the complexities of within-person and between-person dynamics as they unfold over time.

Keywords:

• Conduct problems
• emotional problems
• Millennium Cohort Study
• moderation
• RI-CLPM

Acknowledgements

We are very grateful to all the families who took part in the Millennium Cohort Study, and the whole MCS team, which includes interviewers, computer and laboratory technicians, clerical workers, research scientists, and volunteers.

Ethics approval

All sweeps of the Millennium Cohort Study were approved by the London Multicentre Research Ethics Committee. (Sweep-2: MREC/03/2/022; Sweep-3: 05/MRE02/46; Sweep-4: 07/MRE03/32).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The University of London Centre for Longitudinal Studies owns the copyright for the Millennium Cohort Study (MCS) data used in this study. The MCS data are held/curated by the UK Data Service. Anyone wishing to use the MCS data (found at: https://discover.ukdataservice.ac.uk/series/?sn=2000031) must register and submit a data request to the UK Data Service at http://ukdataservice.ac.uk/. Additional terms and conditions are outlined here: https://www.ukdataservice.ac.uk/get-data/how-to-access/conditions.

Availability of code

Code is available on the Open Science Framework: https://osf.io/tjxrd/.

Preprint

A preprint of this paper is available here: https://doi.org/10.31234/osf.io/wktrb

Additional information

Funding

The Millennium Cohort Study is funded by the UK Economic and Social Research Council. LGS is funded by the Jacobs Foundation. SJB is funded by Wellcome [grant number WT107496/Z/15/Z], the MRC, the Jacobs Foundation, the Wellspring Foundation and the University of Cambridge. RAK is funded by a Hypatia fellowship (RadboudUMC). AU and ALM have no funding to declare for this study. The study sponsors had no part in the design, data analysis and interpretation of this study, in the writing of the manuscript or in the decision to submit the paper for publication. The authors’ work was independent of their funders.