powerMediation (version 0.0.6)

powerMediation.Sobel: Power for testing mediation effect (Sobel's test)

Description

Calculate power for testing mediation effect based on Sobel's test.

Usage

powerMediation.Sobel(n, theta.1a, lambda.a, sigma.x, sigma.m, 
  rho2.mx, sigma.e, sigma.epsilon, alpha = 0.05, verbose = TRUE)

Arguments

n

sample size.

theta.1a

regression coefficient for the predictor in the linear regression linking the predictor $x$ to the mediator $m$ ($m_i=\theta_0+\theta_1 x_i + e_i, e_i\sim N(0, \sigma^2_e)$).

lambda.a

regression coefficient for the mediator in the linear regression linking the predictor $x$ and the mediator $m$ to the outcome $y$ ($y_i=\gamma+\lambda m_i+ \lambda_2 x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma^2_{\epsilon})$).

sigma.x

variance of the predictor.

sigma.m

variance of the mediator

rho2.mx

square of the correlation between the predictor and the mediator.

sigma.e

standard deviation of the random error term in the linear regression linking the predictor $x$ to the mediator $m$ ($m_i=\theta_0+\theta_1 x_i + e_i, e_i\sim N(0, \sigma^2_e)$).

sigma.epsilon

standard deviation of the random error term in the linear regression linking the predictor $x$ and the mediator $m$ to the outcome $y$ ($y_i=\gamma+\lambda m_i+ \lambda_2 x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma^2_{\epsilon})$).

alpha

type I error.

verbose

logical. TRUE means printing power; FALSE means not printing power.

Value

• power
  power of the test for the parameter $\theta_1\lambda$
• delta
  $\theta_1\lambda/(sd(\hat{\theta}_1)sd(\hat{\lambda}))$

Details

The power is for testing the null hypothesis $\theta_1\lambda=0$ versus the alternative hypothesis $\theta_{1a}\lambda_a\neq 0$ for the linear regressions: $$m_i=\theta_0+\theta_1 x_i + e_i, e_i\sim N(0, \sigma^2_e)$$ $$y_i=\gamma+\lambda m_i+ \lambda_2 x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma^2_{\epsilon})$$

Test statistic is based on Sobel's (1982) test: $$Z=\frac{\hat{\theta}_1\hat{\lambda}}{\hat{\sigma}_{\theta_1\lambda}}$$ where $\hat{\sigma}_{\theta_1\lambda}$ is the estimated standard deviation of the estimate $\hat{\theta}_1\hat{\lambda}$ using multivariate delta method: $$\sigma_{\theta_1\lambda}=\sqrt{\theta_1^2\sigma_{\lambda}^2+\lambda^2\sigma_{\theta_1}^2}$$ and $\hat{\sigma}_{\theta_1}=\sigma_e^2/(n\sigma_x^2)$ is the estimated standard deviation of the estimate $\hat{\theta}_1$, and $\hat{\sigma}_{\lambda}=\sigma_{\epsilon}^2/(n\sigma_m^2(1-\rho_{mx}^2))$ is the estimated standard deviation of the estimate $\hat{\lambda}$.

References

Sobel, M. E. Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology. 1982;13:290-312.

See Also

ssMediation.Sobel, testMediation.Sobel

Examples

powerMediation.Sobel(n=100, theta.1a=0.1701, lambda.a=0.1998, 
   sigma.x=0.57, sigma.m=0.61, rho2.mx=0.3, sigma.e=0.2, sigma.epsilon=0.2, 
   alpha = 0.05, verbose = TRUE)