Latent Growth Models with Floors, Ceilings, and Random Knots

In longitudinal/developmental studies, individual growth trajectories are sometimes bounded by a floor at the beginning of the observation period and/or a ceiling toward the end of the observation period (or vice versa), resulting in inherently nonlinear growth patterns. If the trajectories between the floor and ceiling are approximately linear, such longitudinal growth patterns can be described with a linear piecewise (spline) model in which segments join at knots. In these scenarios, it may be of specific interest for researchers to examine the timing when transition occurs, and in some occasions also to examine the levels of the floors and/or ceilings if they are not known and fixed. In the current study, we propose a reparameterized piecewise latent growth curve model so that a direct estimation of the random knots (and, if needed, a direct estimation of random floors and ceilings) is possible. We derive the model reparameterization using a 4-step structured latent curve modeling approach. We provide two illustrative examples to demonstrate how the proposed reparameterized models can be fitted to longitudinal growth data using the popular SEM software Mplus and we supply the full coding for applied researchers' reference.