====== Algorithm Implementation of Power for Model 58 Conditional Processes ======

Power analysis is conducted for the model below:


{{:manual: m58fig.png?600|}}

====== The Model ======

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

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

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 $\theta_{x \to m \to y}=(\beta_1+c_1w)(\beta_2+c_2w)$. 


===== How to use =====

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