Random Intercepts and Slopes in Longitudinal Models: When Are They "Good" and "Bad" Controls?

This study examines the implications of including random components, specifically random intercepts and slopes, in cross-lagged panel models commonly used in longitudinal psychological research. Prior work has shown that the Random-Intercept Cross-Lagged Panel Model (RI-CLPM) can reduce bias in cross-lagged estimates when time-invariant confounders are present. More recent findings suggest that even in the absence of such traits, the RI-CLPM may still produce “illusory” intercept variance that helps mitigate bias from time-varying confounders. Building on this work, we use analytical derivations, simulations, and empirical data to evaluate when random intercepts and slopes act as useful or problematic adjustments. We show that random intercepts can reduce estimation bias under certain conditions but may underestimate longer-lag 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. 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.