Monte Carlo Simulation Parameters (Beta X)
paramsbeta
A data frame with 12 variables
Simulation task identification number.
Shape 1. Beta distribution parameter \(\alpha\).
Shape 2. Beta distribution parameter \(\beta\).
Sample size.
Population mean of x
\(\left( \mu_x \right)\).
Population mean of m
\(\left( \mu_m \right)\).
Population mean of y
\(\left( \mu_y \right)\).
Population slope of path from x
to y
\(\left( \dot{\tau} \right)\)
Population slope of path from m
to y
\(\left( \beta \right)\)
Population slope of path from x
to m
\(\left( \alpha \right)\)
Population variance of x
\(\left( \sigma_{x}^{2} \right)\)
Population variance of m
\(\left( \sigma_{m}^{2} \right)\)
Population variance of y
\(\left( \sigma_{y}^{2} \right)\)
Monte Carlo replications.
The simple mediation model is given by $$ y_i = \delta_y + \dot{\tau} x_i + \beta m_i + \varepsilon_{y_{i}} $$
$$ m_i = \delta_m + \alpha x_i + \varepsilon_{m_{i}} $$
The parameters for the mean structure are $$ \boldsymbol{\theta}_{\text{mean structure}} = \left\{ \mu_x, \delta_m, \delta_y \right\} . $$
The parameters for the covariance structure are $$ \boldsymbol{\theta}_{\text{covariance structure}} = \left\{ \dot{\tau}, \beta, \alpha, \sigma_{x}^{2}, \sigma_{\varepsilon_{m}}^{2}, \sigma_{\varepsilon_{y}}^{2} \right\} . $$
#> taskid shape1 shape2 n mux mum muy taudot beta alpha sigma2x #> 1 1 1.5 1.5 1000 0.5 0.5 0.5 0.1414214 0.7140742 0.7140742 0.0625 #> 2 2 1.5 1.5 500 0.5 0.5 0.5 0.1414214 0.7140742 0.7140742 0.0625 #> 3 3 1.5 1.5 250 0.5 0.5 0.5 0.1414214 0.7140742 0.7140742 0.0625 #> 4 4 1.5 1.5 200 0.5 0.5 0.5 0.1414214 0.7140742 0.7140742 0.0625 #> 5 5 1.5 1.5 150 0.5 0.5 0.5 0.1414214 0.7140742 0.7140742 0.0625 #> 6 6 1.5 1.5 100 0.5 0.5 0.5 0.1414214 0.7140742 0.7140742 0.0625 #> sigma2m sigma2y reps #> 1 0.0625 0.0625 5000 #> 2 0.0625 0.0625 5000 #> 3 0.0625 0.0625 5000 #> 4 0.0625 0.0625 5000 #> 5 0.0625 0.0625 5000 #> 6 0.0625 0.0625 5000#> 'data.frame': 531 obs. of 14 variables: #> $ taskid : int 1 2 3 4 5 6 7 8 9 10 ... #> $ shape1 : num 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 ... #> $ shape2 : num 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 ... #> $ n : num 1000 500 250 200 150 100 75 50 20 1000 ... #> $ mux : num 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ... #> $ mum : num 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ... #> $ muy : num 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ... #> $ taudot : num 0.141 0.141 0.141 0.141 0.141 ... #> $ beta : num 0.714 0.714 0.714 0.714 0.714 ... #> $ alpha : num 0.714 0.714 0.714 0.714 0.714 ... #> $ sigma2x: num 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 ... #> $ sigma2m: num 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 ... #> $ sigma2y: num 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 ... #> $ reps : num 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 ...