  Longitudinal processes are often associated with each other over time;
therefore, it is important to investigate the associations among developmental
processes and understand their joint development. The latent growth curve model
(LGCM) with a time-varying covariate (TVC) provides a method to estimate the
TVC's effect on a longitudinal outcome while simultaneously modeling the
outcome's change. However, it does not allow the TVC to predict variations in
the random growth coefficients. We propose decomposing the TVC's effect into
initial trait and temporal states using three methods to address this
limitation. In each method, the baseline of the TVC is viewed as an initial
trait, and the corresponding effects are obtained by regressing random
intercepts and slopes on the baseline value. Temporal states are characterized
as (1) interval-specific slopes, (2) interval-specific changes, or (3) changes
from the baseline at each measurement occasion, depending on the method. We
demonstrate our methods through simulations and real-world data analyses,
assuming a linear-linear functional form for the longitudinal outcome. The
results demonstrate that LGCMs with a decomposed TVC can provide unbiased and
precise estimates with target confidence intervals. We also provide OpenMx and
Mplus 8 code for these methods with commonly used linear and nonlinear
functions.

Methodology