  The linear spline growth model (LSGM), which approximates complex patterns
using at least two linear segments, is a popular tool for examining nonlinear
change patterns. Among such models, the linear-linear piecewise change pattern
is the most straightforward one. An earlier study has proved that other than
the intercept and slopes, the knot (or change-point), at which two linear
segments join together, can be estimated as a growth factor in a
reparameterized longitudinal model in the latent growth curve modeling
framework. However, the reparameterized coefficients were no longer directly
related to the underlying developmental process and therefore lacked
meaningful, substantive interpretation, although they were simple functions of
the original parameters. This study proposes transformation matrices between
parameters in the original and reparameterized models so that the interpretable
coefficients directly related to the underlying change pattern can be derived
from reparameterized ones. Additionally, the study extends the existing
linear-linear piecewise model to allow for individual measurement occasions,
and investigates predictors for the individual-differences in change patterns.
We present the proposed methods with simulation studies and a real-world data
analysis. Our simulation studies demonstrate that the proposed method can
generally provide an unbiased and consistent estimation of model parameters of
interest and confidence intervals with satisfactory coverage probabilities. An
empirical example using longitudinal mathematics achievement scores shows that
the model can estimate the growth factor coefficients and path coefficients
directly related to the underlying developmental process, thereby providing
meaningful interpretation. For easier implementation, we also provide the
corresponding code for the proposed models.
