A single-level random-effects cross-lagged panel model for longitudinal mediation analysis

Cross-lagged panel models (CLPMs) are widely used to test mediation with longitudinal panel data. One major limitation of the CLPMs is that the model effects are assumed to be fixed across individuals. This assumption is likely to be violated (i.e., the model effects are random across individuals) in practice. When this happens, the CLPMs can potentially yield biased parameter estimates and misleading statistical inferences. This article proposes a model named a random-effects cross-lagged panel model (RE-CLPM) to account for random effects in CLPMs. Simulation studies show that the RE-CLPM outperforms the CLPM in recovering the mean indirect and direct effects in a longitudinal mediation analysis when random effects exist in the population. The performance of the RE-CLPM is robust to a certain degree, even when the random effects are not normally distributed. In addition, the RE-CLPM does not produce harmful results when the model effects are in fact fixed in the population. Implications of the simulation studies and potential directions for future research are discussed.