WITHDRAWN: Empirical Sample Size Guidelines for Latent Difference Score Mediation: A Monte Carlo Study

Introduction: Mediation models are commonly used to identify the mechanisms through which one variable influences another. Mediation analysis is commonly used to model how preventive interventions exert their efforts on a desired outcome through a mediating or target variable. Longitudinal mediation models extend traditional methods by examining how processes unfold overtime. Among longitudinal mediation methods, latent difference score mediation stands out due to its unique ability to capture non-linear change, and both intra- and inter-individual variability. However, there is limited information regarding sample size demands to achieve adequate power with this method, resulting in few applications of latent difference score mediation.

Methods: A Monte Carlo simulation was conducted to examine the required sample size to detect mediation among several variations of the latent difference score mediation model using Mplus statistical software. Ten unique structural models and nine unique population models with varying effect size pairings were evaluated, resulting in a total of 90 unique models. Each model was tested with 1,000 replications and 500 bootstrap draws. Sample sizes were adjusted in an iterative process until adequate statistical power, coverage, and minimal bias was achieved.

Results: Empirical sample estimates ranged from 270 – 780, with sample requirements varying across structural and population models. In general, the structural model complexity had a large impact on the empirical sample size estimates. Further, population models with larger effect sizes tended to require smaller sample sizes than those with smaller effect sizes. Finally, the magnitude of effect for the path influenced sample size estimates more strongly than the effect of the a path.

Conclusions: The current study aimed to offer a generalizable set of sample size guidelines for researchers interested in applying latent difference score mediation models. On the basis of the results from the empirical sample estimates, there three key recommendations for researchers interested in using latent difference score mediation models: (1) simplicity is considered a virtue and thus, difference scores should be included as necessary within any given model; (2) researchers must thoroughly evaluate the literature to determine the expected effect sizes before choosing their sample size; and (3) the empirical sample estimates should be viewed as a lower bound to account for the missing data and nonnormally distributed data.