Total, Direct, and Indirect Effects 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 need the process noise covariance matrix sigma (\(\boldsymbol{\Sigma}\)) to calculate the standardized total, direct, and indirect effects.

sigma <- matrix(
  data = c(
    0.24455556, 0.02201587, -0.05004762,
    0.02201587, 0.07067800, 0.01539456,
    -0.05004762, 0.01539456, 0.07553061
  ),
  nrow = 3,
  ncol = 3
)
sigma

            [,1]       [,2]        [,3]
[1,]  0.24455556 0.02201587 -0.05004762
[2,]  0.02201587 0.07067800  0.01539456
[3,] -0.05004762 0.01539456  0.07553061

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)

Total, Direct, and Indirect Effects in CT-Med

Now, we compute the total, direct, and indirect effects across the sequence of delta_t (\(\Delta t\)), and visualize their dynamic behavior.

med <- Med(
  phi = phi,
  delta_t = delta_t,
  from = "x",
  to = "y",
  med = "m"
)
plot(med)

Standardized Total, Direct, and Indirect Effects in CT-Med

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

med_std <- MedStd(
  phi = phi,
  sigma = sigma,
  delta_t = delta_t,
  from = "x",
  to = "y",
  med = "m"
)
plot(med_std)