The outcome is repeatedly measured in the moderation.
There are two papers explaining the methods behind:
Curran, P. J., Bauer, D. J., & Willoughby, M. T. (2004). Testing main effects and interactions in latent curve analysis. Psychological Methods, 9(2), 220-237.
Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). Computational tools for probing interactions in multiple linear regression, multilevel modeling, and latent curve analysis. Journal of Educational and Behavioral Statistics, 31(4), 437-448.
Note: online tools mentioned in this paper could be found at: http://www.quantpsy.org/interact/index.htm
Though moderation was not a main focus in this classic paper, gender as a moderator appeared in the growth modeling.
- Ployhart, R. E., & Vandenberg, R. J. (2010). Longitudinal research: The theory, design, and analysis of change. Journal of management, 36(1), 94-120.
Two example articles deployed moderation in latent growth modeling:
AMJ: more details in Online Supplemental Materials:
- Deng, Y., Lin, W., Song, Y., Wang, M., Cai, D., & Liu, J. (In press). Socialization as a political arena: A multi-agent interactionist perspective to understand political skill and newcomer socialization rates. Academy of Management Journal.
JAP: Multilevel moderation
- Miron-Spektor, E., Vashdi, D. R., & Gopher, H. (2022). Bright sparks and enquiring minds: Differential effects of goal orientation on the creativity trajectory. Journal of Applied Psychology, 107(2), 310-218.
