A Simulation Study of Mediated Effect Measures

A Simulation Study of Mediated Effect Measures

1995 January 1 | David P. MacKinnon, Ghulam Warsi, and James H. Dwyer
A simulation study was conducted to evaluate the performance of point and variance estimators for mediated effect measures, including the mediated effect, the ratio of mediated to nonmediated effects, and the proportion of the total effect that is mediated. The study compared several approximate solutions based on the multivariate delta method and second-order Taylor series expansions to empirical standard deviations and theoretical standard errors. The simulations involved 500 replications of three normally distributed variables for eight sample sizes (N = 10, 25, 50, 100, 500, 1000, and 5000) and 64 parameter value combinations. The results showed that for sample sizes of at least 50, the standard error estimates of the indirect effect were very similar, except when the independent variable was dichotomized. A sample size of at least 500 was needed for accurate point and variance estimates of the proportion mediated. The point and variance estimates of the ratio of the mediated to nonmediated effect did not stabilize until the sample size was 2,000 for the all continuous variable case. The study also examined the performance of different variance estimators for the mediated effect, including the multivariate delta method, second-order Taylor series, and unbiased variance estimators. The results indicated that the first-order Taylor series estimator performed best for the mediated effect. For the ratio and proportion mediated, the second-order Taylor series estimators were more accurate than the first-order ones. The study found that the standard error estimators for the mediated effect were quite similar across sample sizes, but the McGuigan and Langholtz estimator was approximately two to three times larger than the true standard error for binary independent variables. The proportion of confidence intervals to the left and right of the true value was approximately 5% for all sample sizes, with more confidence intervals to the left of the true value for smaller samples. The study concluded that the mediated effect point estimates had very little bias for all sample sizes, and the standard error estimators were quite close for sample sizes greater than 50. The results also showed that the required sample size varied with the magnitude of effects, and that the proportion and ratio measures were likely to be unstable because they are ratios of random variables rather than products. The study emphasized the importance of using appropriate sample sizes and estimators when analyzing mediated effects in experimental and nonexperimental studies.A simulation study was conducted to evaluate the performance of point and variance estimators for mediated effect measures, including the mediated effect, the ratio of mediated to nonmediated effects, and the proportion of the total effect that is mediated. The study compared several approximate solutions based on the multivariate delta method and second-order Taylor series expansions to empirical standard deviations and theoretical standard errors. The simulations involved 500 replications of three normally distributed variables for eight sample sizes (N = 10, 25, 50, 100, 500, 1000, and 5000) and 64 parameter value combinations. The results showed that for sample sizes of at least 50, the standard error estimates of the indirect effect were very similar, except when the independent variable was dichotomized. A sample size of at least 500 was needed for accurate point and variance estimates of the proportion mediated. The point and variance estimates of the ratio of the mediated to nonmediated effect did not stabilize until the sample size was 2,000 for the all continuous variable case. The study also examined the performance of different variance estimators for the mediated effect, including the multivariate delta method, second-order Taylor series, and unbiased variance estimators. The results indicated that the first-order Taylor series estimator performed best for the mediated effect. For the ratio and proportion mediated, the second-order Taylor series estimators were more accurate than the first-order ones. The study found that the standard error estimators for the mediated effect were quite similar across sample sizes, but the McGuigan and Langholtz estimator was approximately two to three times larger than the true standard error for binary independent variables. The proportion of confidence intervals to the left and right of the true value was approximately 5% for all sample sizes, with more confidence intervals to the left of the true value for smaller samples. The study concluded that the mediated effect point estimates had very little bias for all sample sizes, and the standard error estimators were quite close for sample sizes greater than 50. The results also showed that the required sample size varied with the magnitude of effects, and that the proportion and ratio measures were likely to be unstable because they are ratios of random variables rather than products. The study emphasized the importance of using appropriate sample sizes and estimators when analyzing mediated effects in experimental and nonexperimental studies.
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[slides and audio] A Simulation Study of Mediated Effect Measures.