Jenss-Bayley Latent Change Score Model with Individual Ratio of Growth Acceleration in the Framework of Individual Measurement Occasions

Longitudinal analysis has been widely employed to examine between-individual differences in within-individual change. One challenge of such analyses lies in that the rate-of-change is only available indirectly when change patterns are nonlinear with respect to time. Latent change score models (LCSMs), which can be employed to investigate the change in growth rate at the individual level, have been developed to address this challenge. We extend an existing LCSM with the Jenss-Bayley growth curve (Grimm et al., 2016, Chapter 18) and propose a novel expression of change scores that allows for (1) unequally-spaced study waves and (2) individual measurement occasions around each wave. We also extend the existing model to estimate the individual ratio of growth acceleration (that largely determines the trajectory shape and is viewed as the most important parameter in the Jenss-Bayley model). We present the proposed model by simulation studies and a real-world data analysis. Our simulation studies demonstrate that the proposed model generally estimates the parameters of interest unbiasedly, precisely, and exhibits appropriate confidence interval coverage. More importantly, the proposed model with the novel expression of change scores performed better than the existing model shown by simulation studies. An empirical example using longitudinal reading scores shows that the model can estimate the individual ratio of growth acceleration and generate individual growth rate in practice. We also provide the corresponding code of the proposed model.