An Analytical Comparison of Latent Growth Curve, Cross-Lagged Panel, and Latent Difference Score Modeling for Longitudinal Mediation Analysis

Latent growth curve, cross-lagged panel, and latent difference score models are widely used for longitudinal data analysis. Relationships among those models have been analytically investigated in the extant literature for the univariate and bivariate contexts. However, mathematical connections among these models where three time-varying variables (i.e., input, mediator, outcome) are involved in longitudinal mediation analysis have not been previously studied. To fill in the research gap, we analytically derived the mathematical connections between latent growth curve mediation models and latent difference score mediation models (LDSMMs), as well as those between cross-lagged panel mediation models and LDSMMs for longitudinal mediation analysis. The equivalence relationships among the longitudinal mediation models provided new insights into the connections and interpretations of these models. We provided numerical examples using both simulated and real longitudinal data to illustrate the equivalence relationships, and shared the data and code online. Implications for longitudinal mediation modeling were discussed.