Model-Implied Variance-Covariance Matrix

Model-implied variance-covariance matrix from the simple mediation model.

Sigmathetafromsigma2(taudot, beta, alpha, sigma2x, sigma2m, sigma2y)

Arguments

taudot	Numeric. Slope of path from x to y \(\left( \dot{\tau} \right)\).
beta	Numeric. Slope of path from m to y \(\left( \beta \right)\) .
alpha	Numeric. Slope of path from x to m \(\left( \alpha \right)\) .
sigma2x	Numeric. Variance of x \(\left( \sigma_{x}^{2} \right)\).
sigma2m	Numeric. Variance of m \(\left( \sigma_{m}^{2} \right)\) .
sigma2y	Numeric. Variance of y \(\left( \sigma_{y}^{2} \right)\) .

Details

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 $$ \boldsymbol{\theta}_{\text{covariance structure}} = \left\{ \dot{\tau}, \beta, \alpha, \sigma_{x}^{2}, \sigma_{\varepsilon_{m}}^{2}, \sigma_{\varepsilon_{y}}^{2} \right\} . $$

See also

Other reticular action model functions: A.std(), A(), Mfrommu(), M(), S.std(), Sfromsigma2(), Sigmatheta.std(), Sigmatheta(), S(), mutheta()

Author

Ivan Jacob Agaloos Pesigan

Examples

Sigmathetafromsigma2(
  taudot = 0.207648,
  beta = 0.451039,
  alpha = 0.338593,
  sigma2x = 1.2934694,
  sigma2m = 1.0779592,
  sigma2y = 1.2881633
)
#>           x         m         y
#> x 1.2934694 0.4379597 0.4661232
#> m 0.4379597 1.0779592 0.5771431
#> y 0.4661232 0.5771431 1.2881633
cov(jeksterslabRdatarepo::thirst)
#>             temp    thirst     water
#> temp   1.2934694 0.4379592 0.4661224
#> thirst 0.4379592 1.0779592 0.5771429
#> water  0.4661224 0.5771429 1.2881633