  Longitudinal analysis has been widely employed to examine between-individual
differences in within-individual change. One challenge for 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., 2016c) 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 then 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 for
the proposed model.
