A SIMULATION STUDY OF MEDIATED EFFECT MEASURES

Analytical solutions for point and variance estimators of the mediated effect, the ratio of the mediated to the direct effect, and the propo rtion of the total effect that is mediated were studied with statistic al simulations. We compared several approximate solutions based on the multivariate delta method and second order Taylor series expansions t o the empirical standard deviation of each estimator and theoretical s tandard error when available. The simulations consisted of 500 replica tions of three normally distributed variables for eight sample sizes ( N = 10, 25, 50, 100, 500, 1000, and 5000) and 64 parameter value combi nations. The different solutions for the standard error of the indirec t effect were very similar for sample size of at least 50, except when the independent variable was dichotomized. A sample size of at least 500 was needed for accurate point and variance estimates of the propor tion mediated. The point and variance estimates of the ratio of the me diated to nonmediated effect did not stabilize until the sample size w as 2,000 for the all continuous variable case. Implications for the es timation of mediated effects in experimental and nonexperimental studi es are discussed.