Multilevel Autoregressive Mediation Models: Specification, Estimation, and Applications

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In the current study, extending from the cross-lagged panel models (CLPMs) in Cole and Maxwell (2003), we proposed the multilevel autoregressive mediation models (MAMMs) by allowing the coefficients to differ across individuals. In addition, Level-2 covariates can be included to explain the interindividual differences of mediation effects. Given the complexity of the proposed models, Bayesian estimation was used. Both a CLPM and an unconditional MAMM were fitted to daily diary data. The 2 models yielded different statistical conclusions regarding the average mediation effect. A simulation study was conducted to examine the estimation accuracy of Bayesian estimation for MAMMs and consequences of model mis-specifications. Factors considered included the sample size (N), number of time points (T), fixed indirect and direct effect sizes, and Level-2 variances and covariances. Results indicated that the fixed effect estimates for the indirect effect components (a and b) and the fixed effects of Level-2 covariates were accurate when N ≥ 50 and T ≥ 5. For estimating Level-2 variances and covariances, they were accurate provided a sufficiently large N and T (e.g., N ≥ 500 and T ≥ 50). Estimates of the average mediation effect were generally accurate when N ≥ 100 and T ≥ 10, or N ≥ 50 and T ≥ 20. Furthermore, we found that when Level-2 variances were zero, MAMMs yielded valid inferences about the fixed effects, whereas when random effects existed, CLPMs had low coverage rates for fixed effects. DIC can be used for model selection. Limitations and future directions were discussed.

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