TY - JOUR

T1 - A Simulation Study of Mediated Effect Measures

AU - Mackinnon, David

AU - Warsi, Ghulam

AU - Dwyer, James H.

N1 - Funding Information:
This research was supported by a Public Health Service grant (DA06211). Part of this work was presented at the 1991 Psychometric Society Meeting. We thank Michele Nowling for manuscript preparation and Michael Sobel, Leona Aiken, Sanford Braver, and Steve West for comments on the manuscript. The following derivations can be obtained by writing to the first author: the independence of the estimators a and h, true variances of a and b, and the first and second order Taylor series solutions for the proportion and ratio measures. The first author may be reached at the Department of Psychology, Arizona State University, Tempe, Arizona 85287-1 104.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - Analytical solutions for point and variance estimators of the mediated effect, the ratio of the mediated to the direct effect, and the proportion of the total effect that is mediated were studied with statistical simulations. We compared several approximate solutions based on the multivariate delta method and second order Taylor series expansions to the empirical standard deviation of each estimator and theoretical standard error when available. The simulations consisted of 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 different solutions for the standard error of the indirect effect were very similar for sample sizes 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 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. Implications for the estimation of mediated effects in experimental and nonexperimental studies are discussed.

AB - Analytical solutions for point and variance estimators of the mediated effect, the ratio of the mediated to the direct effect, and the proportion of the total effect that is mediated were studied with statistical simulations. We compared several approximate solutions based on the multivariate delta method and second order Taylor series expansions to the empirical standard deviation of each estimator and theoretical standard error when available. The simulations consisted of 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 different solutions for the standard error of the indirect effect were very similar for sample sizes 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 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. Implications for the estimation of mediated effects in experimental and nonexperimental studies are discussed.

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U2 - 10.1207/s15327906mbr3001_3

DO - 10.1207/s15327906mbr3001_3

M3 - Article

AN - SCOPUS:84948490000

VL - 30

SP - 41

EP - 62

JO - Multivariate Behavioral Research

JF - Multivariate Behavioral Research

SN - 0027-3171

IS - 1

ER -