A Non-Parametric Approach to Modeling Accelerated Longitudinal Designs

Accelerated longitudinal designs (ALDs) offer an efficient means of studying large developmental periods by combining shorter longitudinal samples across overlapping cohorts. ALDs have been used to study processes that span large developmental epochs, such as cognitive development. However, traditional parametric approaches may impose structural assumptions that limit the accurate reconstruction of individual developmental trajectories. We investigate a nonparametric functional data analytic (FDA) approach for modeling latent trajectories in accelerated longitudinal data. This method allows for the recovery of smooth, continuous time trajectories that account for both shared and idiosyncratic patterns of change. We compare the FDA approach to the continuous time latent change score model with simulations that emulate nonlinear change processes often seen in developmental research. We apply both methods to two empirical datasets with individuals aged 5- to 22-years, where each person is assessed two or three times. Our results demonstrate that the FDA method captures the shape and timing of individual trajectories more accurately beyond the observed data. These findings suggest that FDA offers a robust and flexible alternative for modeling developmental change in ALDs.