Random Intercepts and Slopes in Cross-Lagged Panel Models: When Are They "Good" and "Bad" Controls?

This study examines when random components, specifically random intercepts and slopes, function as good versus bad controls in cross-lagged panel models commonly used in longitudinal psychological research. While prior work has focused primarily on time-invariant confounders as the motivation for the Random-Intercept Cross-Lagged Panel Model (RI-CLPM), we argue that omitted processes, unmeasured time-varying variables that co-develop alongside the focal constructs, likely represent a prevalent source of bias in most psychological longitudinal research, yet have received much less systematic attention. We use analytical derivations, simulations, and empirical data to evaluate when random intercepts and slopes function as good versus bad controls under this practically relevant scenario. We show that random intercepts can reduce estimation bias in lag-1 cross-lagged and autoregressive effects in most realistic conditions, but tend to underestimate lag-2 and longer effects by absorbing variance attributable to unmodeled mediating processes. We also find that adding random slopes to the model can introduce additional bias by conditioning on post-treatment variation. This problem might be particularly relevant for the typical psychological panel study, which commonly involves a relatively small number of measurement waves. These results highlight the complexities of correctly specifying longitudinal models of psychological characteristics and offer guidance for researchers using longitudinal panel models to study dynamic psychological processes.