testMediation.Sobel: P-value and confidence interval for testing mediation effect (Sobel's test)

Description

Calculate p-value and confidence interval for testing mediation effect based on Sobel's test.

Usage

testMediation.Sobel(theta.1.hat, 
                    lambda.hat, 
                    sigma.theta1, 
                    sigma.lambda, 
                    alpha = 0.05)

Arguments

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.

Value

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 $\theta_1\lambda$.

Details

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 $\hat{\lambda}$.

References

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

Examples

Run this code

# NOT RUN {
  testMediation.Sobel(theta.1.hat=0.1701, lambda.hat=0.1998, 
    sigma.theta1=0.01, sigma.lambda=0.02, alpha=0.05)
# }

Run the code above in your browser using DataLab