MCTotalCentral: Monte Carlo Sampling Distribution of Total Effect Centrality...
In cTMed: Continuous-Time Mediation

MCTotalCentral

R Documentation

Monte Carlo Sampling Distribution of Total Effect Centrality Over a Specific Time Interval or a Range of Time Intervals

Description

This function generates a Monte Carlo method sampling distribution of the total effect centrality at a particular time interval \Delta t using the first-order stochastic differential equation model drift matrix \boldsymbol{\Phi}.

Usage

MCTotalCentral(
  phi,
  vcov_phi_vec,
  delta_t,
  R,
  test_phi = TRUE,
  ncores = NULL,
  seed = NULL,
  tol = 0.01
)

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)`.
`delta_t`	Numeric. Time interval (`\Delta t`).
`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.
`tol`	Numeric. Smallest possible time interval to allow.

Details

See TotalCentral() for more 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) .

Let \mathbf{g} \left( \hat{\boldsymbol{\theta}} \right) be a parameter that is a function of the estimated parameters. A sampling distribution of \mathbf{g} \left( \hat{\boldsymbol{\theta}} \right) , which we refer to as \mathbf{g} \left( \hat{\boldsymbol{\theta}}^{\ast} \right) , can be generated by using the simulated estimates to calculate \mathbf{g}. The standard deviations of the simulated estimates are the standard errors. Percentiles corresponding to 100 \left( 1 - \alpha \right) \% are the confidence intervals.

Value

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

call: Function call.
args: Function arguments.
fun: Function used ("MCTotalCentral").
output: A list the length of which is equal to the length of delta_t.

Each element in the output list has the following elements:

est: A vector of total effect centrality.
thetahatstar: A matrix of Monte Carlo total effect centrality.

Author(s)

Ivan Jacob Agaloos Pesigan

References

Bollen, K. A. (1987). Total, direct, and indirect effects in structural equation models. Sociological Methodology, 17, 37. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/271028")}

Deboeck, P. R., & Preacher, K. J. (2015). No need to be discrete: A method for continuous time mediation analysis. Structural Equation Modeling: A Multidisciplinary Journal, 23 (1), 61–75. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10705511.2014.973960")}

Ryan, O., & Hamaker, E. L. (2021). Time to intervene: A continuous-time approach to network analysis and centrality. Psychometrika, 87 (1), 214–252. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11336-021-09767-0")}

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")
vcov_phi_vec <- matrix(
  data = c(
    0.00843, 0.00040, -0.00151,
    -0.00600, -0.00033, 0.00110,
    0.00324, 0.00020, -0.00061,
    0.00040, 0.00374, 0.00016,
    -0.00022, -0.00273, -0.00016,
    0.00009, 0.00150, 0.00012,
    -0.00151, 0.00016, 0.00389,
    0.00103, -0.00007, -0.00283,
    -0.00050, 0.00000, 0.00156,
    -0.00600, -0.00022, 0.00103,
    0.00644, 0.00031, -0.00119,
    -0.00374, -0.00021, 0.00070,
    -0.00033, -0.00273, -0.00007,
    0.00031, 0.00287, 0.00013,
    -0.00014, -0.00170, -0.00012,
    0.00110, -0.00016, -0.00283,
    -0.00119, 0.00013, 0.00297,
    0.00063, -0.00004, -0.00177,
    0.00324, 0.00009, -0.00050,
    -0.00374, -0.00014, 0.00063,
    0.00495, 0.00024, -0.00093,
    0.00020, 0.00150, 0.00000,
    -0.00021, -0.00170, -0.00004,
    0.00024, 0.00214, 0.00012,
    -0.00061, 0.00012, 0.00156,
    0.00070, -0.00012, -0.00177,
    -0.00093, 0.00012, 0.00223
  ),
  nrow = 9
)

# Specific time interval ----------------------------------------------------
MCTotalCentral(
  phi = phi,
  vcov_phi_vec = vcov_phi_vec,
  delta_t = 1,
  R = 100L # use a large value for R in actual research
)

# Range of time intervals ---------------------------------------------------
mc <- MCTotalCentral(
  phi = phi,
  vcov_phi_vec = vcov_phi_vec,
  delta_t = 1:5,
  R = 100L # use a large value for R in actual research
)
plot(mc)

# Methods -------------------------------------------------------------------
# MCTotalCentral has a number of methods including
# print, summary, confint, and plot
print(mc)
summary(mc)
confint(mc, level = 0.95)
plot(mc)

cTMed documentation built on Nov. 5, 2025, 7:18 p.m.