MCPhi: Generate Random Drift Matrices Using the Monte Carlo Method

In cTMed: Continuous Time Mediation

Generate Random Drift Matrices Using the Monte Carlo Method

Description

This function generates random drift matrices \boldsymbol{\Phi} using the Monte Carlo method.

Usage

MCPhi(phi, vcov_phi_vec, R, test_phi = TRUE, ncores = NULL, seed = NULL)

Arguments

phi	Numeric matrix. The drift matrix (\boldsymbol{\Phi}). phi should have row and column names pertaining to the variables in the system.
vcov_phi_vec	Numeric matrix. The sampling variance-covariance matrix of \mathrm{vec} \left( \boldsymbol{\Phi} \right).
R	Positive integer. Number of replications.
test_phi	Logical. If test_phi = TRUE, the function tests the stability of the generated drift matrix \boldsymbol{\Phi}. If the test returns FALSE, the function generates a new drift matrix \boldsymbol{\Phi} and runs the test recursively until the test returns TRUE.
ncores	Positive integer. Number of cores to use. If ncores = NULL, use a single core. Consider using multiple cores when number of replications R is a large value.
seed	Random seed.

Details

Monte Carlo Method

Let \boldsymbol{\theta} be \mathrm{vec} \left( \boldsymbol{\Phi} \right), that is, the elements of the \boldsymbol{\Phi} matrix in vector form sorted column-wise. Let \hat{\boldsymbol{\theta}} be \mathrm{vec} \left( \hat{\boldsymbol{\Phi}} \right). Based on the asymptotic properties of maximum likelihood estimators, we can assume that estimators are normally distributed around the population parameters.

\hat{\boldsymbol{\theta}} \sim \mathcal{N} \left( \boldsymbol{\theta}, \mathbb{V} \left( \hat{\boldsymbol{\theta}} \right) \right)

Using this distributional assumption, a sampling distribution of \hat{\boldsymbol{\theta}} which we refer to as \hat{\boldsymbol{\theta}}^{\ast} can be generated by replacing the population parameters with sample estimates, that is,

\hat{\boldsymbol{\theta}}^{\ast} \sim \mathcal{N} \left( \hat{\boldsymbol{\theta}}, \hat{\mathbb{V}} \left( \hat{\boldsymbol{\theta}} \right) \right) .

Value

Returns an object of class ctmedmc which is a list with the following elements:

call

Function call.

args

Function arguments.

fun

Function used ("MCPhi").

output

A list simulated drift matrices.

Author(s)

Ivan Jacob Agaloos Pesigan

See Also

Other Continuous Time Mediation Functions: DeltaBeta(), DeltaIndirectCentral(), DeltaMed(), DeltaTotalCentral(), Direct(), Indirect(), IndirectCentral(), MCBeta(), MCIndirectCentral(), MCMed(), MCTotalCentral(), Med(), PosteriorBeta(), PosteriorIndirectCentral(), PosteriorMed(), PosteriorPhi(), PosteriorTotalCentral(), Total(), TotalCentral(), Trajectory()

Examples

set.seed(42)
phi <- matrix(
  data = c(
    -0.357, 0.771, -0.450,
    0.0, -0.511, 0.729,
    0, 0, -0.693
  ),
  nrow = 3
)
colnames(phi) <- rownames(phi) <- c("x", "m", "y")
MCPhi(
  phi = phi,
  vcov_phi_vec = 0.1 * diag(9),
  R = 100L # use a large value for R in actual research
)
phi <- matrix(
  data = c(
    -6, 5.5, 0, 0,
    1.25, -2.5, 5.9, -7.3,
    0, 0, -6, 2.5,
    5, 0, 0, -6
  ),
  nrow = 4
)
colnames(phi) <- rownames(phi) <- paste0("y", 1:4)
MCPhi(
  phi = phi,
  vcov_phi_vec = 0.1 * diag(16),
  R = 100L, # use a large value for R in actual research
  test_phi = FALSE
)

cTMed documentation built on Oct. 21, 2024, 5:08 p.m.