Total and Indirect Effect Centrality Measures in CT-Med

Installing Required Packages

Before proceeding, ensure that the necessary package are installed and loaded. We use cTMed for calculating total, direct, and indirect effects in continuous-time mediation model.

library(cTMed)

Extracting Matrices for Use in cTMed

We begin by defining the drift matrix phi (\(\boldsymbol{\Phi}\)).

phi <- matrix(
  data = c(
    -0.357, 0.771, -0.450,
    0.000, -0.511, 0.729,
    0.000, 0.000, -0.693
  ),
  nrow = 3,
  ncol = 3
)
phi

       [,1]   [,2]   [,3]
[1,] -0.357  0.000  0.000
[2,]  0.771 -0.511  0.000
[3,] -0.450  0.729 -0.693

Next, we assign row and column names to phi (\(\boldsymbol{\Phi}\)), which will be used to index the matrix.

colnames(phi) <- rownames(phi) <- c("x", "m", "y")
phi

       x      m      y
x -0.357  0.000  0.000
m  0.771 -0.511  0.000
y -0.450  0.729 -0.693

We then create a sequence of time intervals delta_t (\(\Delta t\)) ranging from 0.01 to 10, with a total of 1,000 equally spaced values.

delta_t <- seq(from = 0.01, to = 10, length.out = 1000)

Let’s calculate total and indirect effects centrality for the sequence of delta_t (\(\Delta t\)). We plot to visualize the dynamics.

Total Effect Centrality

total_central <- TotalCentral(
  phi = phi,
  delta_t = delta_t
)
plot(total_central)

Indirect Effect Centrality

indirect_central <- IndirectCentral(
  phi = phi,
  delta_t = delta_t
)
plot(indirect_central)