Power analysis is conducted for the model below:

$m=\beta_1x +a_1w+c_1xw+e_1$

$y=a_2w+\beta_3x+\beta_2m+c_2mw+e_2$

In model 58, both the first-stage path from the predictor $x$ to the mediator $m$ and the second-stage path from the mediator $m$ to the dependent variable $y$ are dependent on the moderator $w$. In this model, the conditional indirect effect of $x$ on $y$ through m is $\theta_{x \to m \to y}=(\beta_1+c_1w)(\beta_2+c_2w)$.

We developed a web app based on wp.modmed.m8 function in the WebPower package. The input of the web app include the following:

• Sample Size
• Significance Level(alpha): the default value is 0.05.
• Number of Simulations
• Regression coefficient of mediator (m) on predictor (x)
• Regression coefficient of outcome (y) on predictor (x)
• Regression coefficient of outcome (y) on mediator (m)
• Regression coefficient of outcome (y) on mediator (w)
• Regression coefficient of mediator (m) on product (xw)
• Regression coefficient of mediator (m) on moderator (w)
• Regression coefficient of mediator (y) on the product (mw)
• Variance of predictor (x)
• Variance of moderator (w)
• Variance of error in the first regression equation
• Variance of error in the second regression equation
• Covariance between predictor (x) and moderator (w)
• Moderator value
• Method