Description Usage Arguments Details Value Note Author(s) References See Also Examples
View source: R/powerMediation.R
Calculate power for testing mediation effect based on Sobel's test.
1 2 3 4 5 6 7 8  powerMediation.Sobel(n,
theta.1a,
lambda.a,
sigma.x,
sigma.m,
sigma.epsilon,
alpha = 0.05,
verbose = TRUE)

n 
sample size. 
theta.1a 
regression coefficient for the predictor in the linear regression linking the predictor x to the mediator m (m_i=θ_0+θ_{1a} x_i + e_i, e_i\sim N(0, σ^2_e)). 
lambda.a 
regression coefficient for the mediator in the linear regression linking the predictor x and the mediator m to the outcome y (y_i=γ+λ_{a} m_i+ λ_2 x_i + ε_i, ε_i\sim N(0, σ^2_{ε})). 
sigma.x 
standard deviation of the predictor. 
sigma.m 
standard deviation of the mediator. 
sigma.epsilon 
standard deviation of the random error term in the linear regression linking the predictor x and the mediator m to the outcome y (y_i=γ+λ_a m_i+ λ_2 x_i + ε_i, ε_i\sim N(0, σ^2_{ε})). 
alpha 
type I error. 
verbose 
logical. 
The power is for testing the null hypothesis θ_1λ=0 versus the alternative hypothesis θ_{1a}λ_a\neq 0 for the linear regressions:
m_i=θ_0+θ_{1a} x_i + e_i, e_i\sim N(0, σ^2_e)
y_i=γ+λ_a m_i+ λ_2 x_i + ε_i, ε_i\sim N(0, σ^2_{ε})
Test statistic is based on Sobel's (1982) test:
Z=\frac{\hat{θ}_{1a}\hat{λ_a}}{\hat{σ}_{θ_{1a}λ_a}}
where \hat{σ}_{θ_{1a}λ_a} is the estimated standard deviation of the estimate \hat{θ}_{1a}\hat{λ_a} using multivariate delta method:
σ_{θ_{1a}λ_a}=√{θ_{1a}^2σ_{λ_a}^2+λ_a^2σ_{θ_{1a}}^2}
and σ_{θ_{1a}}^2=σ_e^2/(nσ_x^2) is the variance of the estimate \hat{θ}_{1a}, and σ_{λ_a}^2=σ_{ε}^2/(nσ_m^2(1ρ_{mx}^2)) is the variance of the estimate \hat{λ_a}, σ_m^2 is the variance of the mediator m_i.
From the linear regression m_i=θ_0+θ_{1a} x_i+e_i, we have the relationship σ_e^2=σ_m^2(1ρ^2_{mx}). Hence, we can simply the variance σ_{θ_{1a}, λ_a} to
σ_{θ_{1a}λ_a}=√{θ_{1a}^2\frac{σ_{ε}^2}{nσ_m^2(1ρ_{mx}^2)}+λ_a^2\frac{σ_{m}^2(1ρ_{mx}^2)}{nσ_x^2}}
power 
power of the test for the parameter θ_{1a}λ_a 
delta 
θ_1λ/(sd(\hat{θ}_{1a})sd(\hat{λ}_a)) 
The test is a twosided test. For onesided tests, please double the
significance level. For example, you can set alpha=0.10
to obtain onesided test at 5% significance level.
Weiliang Qiu stwxq@channing.harvard.edu
Sobel, M. E. Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology. 1982;13:290312.
ssMediation.Sobel
,
testMediation.Sobel
1 2 3  powerMediation.Sobel(n=248, theta.1a=0.1701, lambda.a=0.1998,
sigma.x=0.57, sigma.m=0.61, sigma.epsilon=0.2,
alpha = 0.05, verbose = TRUE)

[1] 0.6876486
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