Accounting for Time-Varying Inter-Individual Differences of Trajectories when Assessing Cross-Lagged Models

This paper explores relationships amongst cross-lagged models allowing trajectories to be freely estimated, some accounting for time-varying differences amongst individuals (Autoregressive Latent Trajectory (ALT), General Cross-lagged Model (GCLM), and Latent Growth Curve Model with Structured Residuals and Unspecified Growth Trajectory (LGCM-SR-UGT)) and some not (Cross-lagged Panel Model (CLPM), Random Intercept Cross-lagged Panel Model (RI-CLPM), and Mean Stationary GCLM). An applied example using LSAY data demonstrates these models. Simulations examine (1) fit indices assessing “good” fit and Bayes Factor for model selection; (2) consequences of ignoring variability in trajectories on cross-lagged estimates. Findings were (1) RMSEA discerned “good” fit and Bayes Factor tended to select models closely related to true model over less related models; (2) various patterns of bias in path estimates and standard errors are found, in particular, causal dominance in conjunction with time-variant between-person variance and covariance were notably influential on bias in path estimates.