🤖 AI Summary
Existing latent growth curve models (LGCMs) struggle to disentangle the baseline trait effect from the dynamic time-varying effect of time-varying covariates (TVCs) on longitudinal outcomes, particularly failing to model how TVCs explain variability in random intercepts and slopes. To address this, we propose a systematic decomposition framework that partitions each TVC into: (1) a baseline effect predicting random intercepts and slopes; and (2) three distinct time-varying effects—interval-level slope, interval-level change, and deviation-from-baseline change. This is the first approach to explicitly model TVC contributions to growth parameter variability within the LGCM framework, supporting both linear and common nonlinear growth trajectories. Implementation is provided for OpenMx and Mplus 8. Simulation and empirical studies demonstrate unbiased parameter estimates, high precision, and confidence interval coverage near nominal levels. All code is publicly available to ensure reproducibility and facilitate extension.
📝 Abstract
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 traditional latent growth curve model (LGCM) with a time-varying covariate (TVC) provides a method to estimate the TVC effect on a longitudinal outcome while 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 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 (a) interval-specific slopes, (b) interval-specific changes, or (c) 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.