testMediation.Sobel: P-value and confidence interval for testing mediation effect...

In powerMediation: Power/Sample Size Calculation for Mediation Analysis

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=θ_0+θ_1 x_i + e_i, e_i\sim N(0, σ^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=γ+λ m_i+ λ_2 x_i + ε_i, ε_i\sim N(0, σ^2_{ε})).
sigma.theta1	standard deviation of \hat{θ}_1 in the linear regression linking the predictor x to the mediator m (m_i=θ_0+θ_1 x_i + e_i, e_i\sim N(0, σ^2_e)).
sigma.lambda	standard deviation of \hat{λ} in the linear regression linking the predictor x and the mediator m to the outcome y (y_i=γ+λ m_i+ λ_2 x_i + ε_i, ε_i\sim N(0, σ^2_{ε})).
alpha	significance level of a test.

Details

The test 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_1 x_i + e_i, e_i\sim N(0, σ^2_e)

y_i=γ+λ 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}_1\hat{λ}}{\hat{σ}_{θ_1λ}}

where \hat{σ}_{θ_1λ} is the estimated standard deviation of the estimate \hat{θ}_1\hat{λ} using multivariate delta method:

σ_{θ_1λ}=√{θ_1^2σ_{λ}^2+λ^2σ_{θ_1}^2}

and \hat{σ}_{θ_1} is the estimated standard deviation of the estimate \hat{θ}_1, and \hat{σ}_{λ} is the estimated standard deviation of the estimate \hat{λ}.

Value

pval	p-value for testing the null hypothesis θ_1λ=0 versus the alternative hypothesis θ_{1a}λ_a\neq 0.
CI.low	Lower bound of the 100 (1-α)\% confidence interval for the parameter θ_1λ.
CI.upp	Upper bound of the 100 (1-α)\% confidence interval for the parameter θ_1λ.

Note

The test is a two-sided test. For one-sided tests, please double the significance level. For example, you can set alpha=0.10 to obtain one-sided test at 5% significance level.

Author(s)

Weiliang Qiu [e-mail]

References

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

See Also

powerMediation.Sobel, ssMediation.Sobel

Examples

  testMediation.Sobel(theta.1.hat=0.1701, lambda.hat=0.1998, 
    sigma.theta1=0.01, sigma.lambda=0.02, alpha=0.05)

Example output

$pval
[1] 0

$CI.low
[1] 0.02625328

$CI.upp
[1] 0.04171868

powerMediation documentation built on March 24, 2021, 1:06 a.m.