Autoregressive mediation models using composite scores and latent variables: Comparisons and recommendations

Area of Science:

• Psychometrics
• Structural Equation Modeling
• Longitudinal Data Analysis

Background:

• Longitudinal mediation analysis is crucial for understanding temporal relationships between variables.
• Existing autoregressive mediation models (AMM) include the uncorrected composite model (UCM), corrected composite model (CCM), and latent variable model (LVM).
• Assessing the accuracy and practical utility of these AMM approaches is essential for reliable research findings.

Purpose of the Study:

• To analytically and empirically compare the performance of UCM, CCM, and LVM in longitudinal mediation analysis.
• To evaluate the accuracy of direct and indirect effect estimates and parameter coverage rates under various conditions.
• To determine the most suitable model for longitudinal mediation analysis based on accuracy, simplicity, and robustness.

Main Methods:

• Analytical derivations of direct and indirect effect estimates for UCM and CCM under unidimensional measurement assumptions.
• A simulation study examining parameter estimation accuracy and coverage rates across different levels of measurement invariance, sample sizes, time points, and reliabilities.
• Comparison of CCM and LVM regarding model complexity, sensitivity to sample size, and overall fit.

Main Results:

• UCM demonstrated asymptotically biased direct and indirect effect estimates when measurement error was present.
• CCM provided asymptotically unbiased estimates when measurement invariance held, comparable to LVM.
• CCM and LVM showed accurate estimates and good coverage, while UCM was not recommended due to inaccuracies.
• CCM exhibited simpler model structure and less sensitivity to sample size compared to LVM.

Conclusions:

• CCM is a recommended approach for longitudinal mediation analysis, offering accurate and robust parameter estimation.
• UCM should be avoided due to its tendency to produce biased estimates in longitudinal mediation.
• CCM presents a practical and statistically sound alternative to LVM, particularly when measurement invariance is met.