Panel models in structural equation modeling that combine static and dynamic components for investigating reciprocal relations while controlling for time-invariant unobserved heterogeneity are becoming increasingly popular. Recently, the Latent Curve Model with Structured Residuals and the Random-Intercept Cross-Lagged Panel Model were suggested as ‘residual-level’ versions of the more traditional Autoregressive Latent Trajectory and Dynamic Panel Models, respectively. Their main benefit is that they allow for a more straightforward interpretation of the trajectory factors. It is not widely known, however, that the residual-level models place potentially strong assumptions on the initial conditions, i.e., the process that was occurring before the observation period began. If the process under investigation is nonstationary (e.g., growing exponentially), has not been going on for long enough to reach equilibrium, or has been ‘knocked’ out of equilibrium, potentially due to an intervention, then the residual-level models are not appropriate. This is shown analytically and with demonstrations using real data. A simple amendment is suggested to relax the assumptions on the initial conditions while retaining the models’ beneficial aspects.
Equivalent approaches to dealing with unobserved heterogeneity in cross-lagged panel models? Investigating the benefits and drawbacks of the latent curve model with structured residuals and the random intercept cross-lagged panel model.
