testMediation.Sobel {powerMediation} | R Documentation |
Calculate p-value and confidence interval for testing mediation effect based on Sobel's test.
testMediation.Sobel(theta.1.hat, lambda.hat, sigma.theta1, sigma.lambda, alpha=0.05)
theta.1.hat |
estimated 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.hat |
estimated 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.theta1 |
standard deviation of \hat{\theta}_1 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.lambda |
standard deviation of \hat{\lambda} 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 |
significance level of a test. |
The test 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} is the estimated standard deviation of the estimate \hat{\theta}_1, and \hat{\sigma}_{\lambda} is the estimated standard deviation of the estimate \hat{\lambda}.
pval |
p-value for testing the null hypothesis \theta_1\lambda=0 versus the alternative hypothesis \theta_{1a}\lambda_a\neq 0. |
CI.low |
Lower bound of the 100 (1-\alpha)\% confidence interval for the parameter \theta_1\lambda. |
CI.upp |
Upper bound of the 100 (1-\alpha)\% confidence interval for the parameter \theta_1\lambda. |
The test is a two-sided test. Code for one-sided tests will be added later.
Weiliang Qiu stwxq@channing.harvard.edu
Sobel, M. E. Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology. 1982;13:290-312.
powerMediation.Sobel
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ssMediation.Sobel
testMediation.Sobel(theta.1.hat=0.1701, lambda.hat=0.1998, sigma.theta1=0.05, sigma.lambda=0.05, alpha=0.05)