Med: Total, Direct, and Indirect Effects of X on Y Through M Over...
In cTMed: Continuous-Time Mediation
Med R Documentation
Total, Direct, and Indirect Effects of X on Y
Through M
Over a Specific Time Interval
or a Range of Time Intervals
Description
This function computes the total, direct, and indirect effects
of the independent variable X
on the dependent variable Y
through mediator variables \mathbf{m}
over a specific time interval \Delta t
or a range of time intervals
using the first-order stochastic differential equation model's
drift matrix \boldsymbol{\Phi}.
Usage
Med(phi, delta_t, from, to, med, 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.
delta_t
Vector of positive numbers.
Time interval
(\Delta t).
from
Character string.
Name of the independent variable X in phi.
to
Character string.
Name of the dependent variable Y in phi.
med
Character vector.
Name/s of the mediator variable/s in phi.
tol
Numeric.
Smallest possible time interval to allow.
Details
See Total(),
Direct(), and
Indirect() for more details.
Linear Stochastic Differential Equation Model
The measurement model is given by
\mathbf{y}_{i, t}
=
\boldsymbol{\nu}
+
\boldsymbol{\Lambda}
\boldsymbol{\eta}_{i, t}
+
\boldsymbol{\varepsilon}_{i, t},
\quad
\mathrm{with}
\quad
\boldsymbol{\varepsilon}_{i, t}
\sim
\mathcal{N}
\left(
\mathbf{0},
\boldsymbol{\Theta}
\right)
where
\mathbf{y}_{i, t},
\boldsymbol{\eta}_{i, t},
and
\boldsymbol{\varepsilon}_{i, t}
are random variables
and
\boldsymbol{\nu},
\boldsymbol{\Lambda},
and
\boldsymbol{\Theta}
are model parameters.
\mathbf{y}_{i, t}
represents a vector of observed random variables,
\boldsymbol{\eta}_{i, t}
a vector of latent random variables,
and
\boldsymbol{\varepsilon}_{i, t}
a vector of random measurement errors,
at time t and individual i.
\boldsymbol{\nu}
denotes a vector of intercepts,
\boldsymbol{\Lambda}
a matrix of factor loadings,
and
\boldsymbol{\Theta}
the covariance matrix of
\boldsymbol{\varepsilon}.
An alternative representation of the measurement error
is given by
\boldsymbol{\varepsilon}_{i, t}
=
\boldsymbol{\Theta}^{\frac{1}{2}}
\mathbf{z}_{i, t},
\quad
\mathrm{with}
\quad
\mathbf{z}_{i, t}
\sim
\mathcal{N}
\left(
\mathbf{0},
\mathbf{I}
\right)
where
\mathbf{z}_{i, t} is a vector of
independent standard normal random variables and
\left( \boldsymbol{\Theta}^{\frac{1}{2}} \right)
\left( \boldsymbol{\Theta}^{\frac{1}{2}} \right)^{\prime}
=
\boldsymbol{\Theta} .
The dynamic structure is given by
\mathrm{d} \boldsymbol{\eta}_{i, t}
=
\left(
\boldsymbol{\iota}
+
\boldsymbol{\Phi}
\boldsymbol{\eta}_{i, t}
\right)
\mathrm{d}t
+
\boldsymbol{\Sigma}^{\frac{1}{2}}
\mathrm{d}
\mathbf{W}_{i, t}
where
\boldsymbol{\iota}
is a term which is unobserved and constant over time,
\boldsymbol{\Phi}
is the drift matrix
which represents the rate of change of the solution
in the absence of any random fluctuations,
\boldsymbol{\Sigma}
is the matrix of volatility
or randomness in the process, and
\mathrm{d}\boldsymbol{W}
is a Wiener process or Brownian motion,
which represents random fluctuations.
Value
Returns an object
of class ctmedmed which is a list with the following elements:
- call
Function call.
- args
Function arguments.
- fun
Function used ("Med").
- output
A matrix of total, direct, and indirect effects.
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")}
See Also
Other Continuous-Time Mediation Functions:
BootBeta(),
BootBetaStd(),
BootIndirectCentral(),
BootMed(),
BootMedStd(),
BootTotalCentral(),
DeltaBeta(),
DeltaBetaStd(),
DeltaIndirectCentral(),
DeltaMed(),
DeltaMedStd(),
DeltaTotalCentral(),
Direct(),
DirectStd(),
Indirect(),
IndirectCentral(),
IndirectStd(),
MCBeta(),
MCBetaStd(),
MCIndirectCentral(),
MCMed(),
MCMedStd(),
MCPhi(),
MCPhiSigma(),
MCTotalCentral(),
MedStd(),
PosteriorBeta(),
PosteriorIndirectCentral(),
PosteriorMed(),
PosteriorTotalCentral(),
Total(),
TotalCentral(),
TotalStd(),
Trajectory()
Examples
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")
# Specific time interval ----------------------------------------------------
Med(
phi = phi,
delta_t = 1,
from = "x",
to = "y",
med = "m"
)
# Range of time intervals ---------------------------------------------------
med <- Med(
phi = phi,
delta_t = 1:30,
from = "x",
to = "y",
med = "m"
)
plot(med)
# Methods -------------------------------------------------------------------
# Med has a number of methods including
# print, summary, and plot
med <- Med(
phi = phi,
delta_t = 1:5,
from = "x",
to = "y",
med = "m"
)
print(med)
summary(med)
plot(med)
cTMed documentation built on Nov. 5, 2025, 7:18 p.m.
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| Med | R Documentation |
Total, Direct, and Indirect Effects of X on Y Through M Over a Specific Time Interval or a Range of Time Intervals
Description
This function computes the total, direct, and indirect effects
of the independent variable X
on the dependent variable Y
through mediator variables \mathbf{m}
over a specific time interval \Delta t
or a range of time intervals
using the first-order stochastic differential equation model's
drift matrix \boldsymbol{\Phi}.
Usage
Med(phi, delta_t, from, to, med, tol = 0.01)
Arguments
phi |
Numeric matrix.
The drift matrix ( |
delta_t |
Vector of positive numbers.
Time interval
( |
from |
Character string.
Name of the independent variable |
to |
Character string.
Name of the dependent variable |
med |
Character vector.
Name/s of the mediator variable/s in |
tol |
Numeric. Smallest possible time interval to allow. |
Details
See Total(),
Direct(), and
Indirect() for more details.
Linear Stochastic Differential Equation Model
The measurement model is given by
\mathbf{y}_{i, t}
=
\boldsymbol{\nu}
+
\boldsymbol{\Lambda}
\boldsymbol{\eta}_{i, t}
+
\boldsymbol{\varepsilon}_{i, t},
\quad
\mathrm{with}
\quad
\boldsymbol{\varepsilon}_{i, t}
\sim
\mathcal{N}
\left(
\mathbf{0},
\boldsymbol{\Theta}
\right)
where
\mathbf{y}_{i, t},
\boldsymbol{\eta}_{i, t},
and
\boldsymbol{\varepsilon}_{i, t}
are random variables
and
\boldsymbol{\nu},
\boldsymbol{\Lambda},
and
\boldsymbol{\Theta}
are model parameters.
\mathbf{y}_{i, t}
represents a vector of observed random variables,
\boldsymbol{\eta}_{i, t}
a vector of latent random variables,
and
\boldsymbol{\varepsilon}_{i, t}
a vector of random measurement errors,
at time t and individual i.
\boldsymbol{\nu}
denotes a vector of intercepts,
\boldsymbol{\Lambda}
a matrix of factor loadings,
and
\boldsymbol{\Theta}
the covariance matrix of
\boldsymbol{\varepsilon}.
An alternative representation of the measurement error is given by
\boldsymbol{\varepsilon}_{i, t}
=
\boldsymbol{\Theta}^{\frac{1}{2}}
\mathbf{z}_{i, t},
\quad
\mathrm{with}
\quad
\mathbf{z}_{i, t}
\sim
\mathcal{N}
\left(
\mathbf{0},
\mathbf{I}
\right)
where
\mathbf{z}_{i, t} is a vector of
independent standard normal random variables and
\left( \boldsymbol{\Theta}^{\frac{1}{2}} \right)
\left( \boldsymbol{\Theta}^{\frac{1}{2}} \right)^{\prime}
=
\boldsymbol{\Theta} .
The dynamic structure is given by
\mathrm{d} \boldsymbol{\eta}_{i, t}
=
\left(
\boldsymbol{\iota}
+
\boldsymbol{\Phi}
\boldsymbol{\eta}_{i, t}
\right)
\mathrm{d}t
+
\boldsymbol{\Sigma}^{\frac{1}{2}}
\mathrm{d}
\mathbf{W}_{i, t}
where
\boldsymbol{\iota}
is a term which is unobserved and constant over time,
\boldsymbol{\Phi}
is the drift matrix
which represents the rate of change of the solution
in the absence of any random fluctuations,
\boldsymbol{\Sigma}
is the matrix of volatility
or randomness in the process, and
\mathrm{d}\boldsymbol{W}
is a Wiener process or Brownian motion,
which represents random fluctuations.
Value
Returns an object
of class ctmedmed which is a list with the following elements:
- call
Function call.
- args
Function arguments.
- fun
Function used ("Med").
- output
A matrix of total, direct, and indirect effects.
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")}
See Also
Other Continuous-Time Mediation Functions:
BootBeta(),
BootBetaStd(),
BootIndirectCentral(),
BootMed(),
BootMedStd(),
BootTotalCentral(),
DeltaBeta(),
DeltaBetaStd(),
DeltaIndirectCentral(),
DeltaMed(),
DeltaMedStd(),
DeltaTotalCentral(),
Direct(),
DirectStd(),
Indirect(),
IndirectCentral(),
IndirectStd(),
MCBeta(),
MCBetaStd(),
MCIndirectCentral(),
MCMed(),
MCMedStd(),
MCPhi(),
MCPhiSigma(),
MCTotalCentral(),
MedStd(),
PosteriorBeta(),
PosteriorIndirectCentral(),
PosteriorMed(),
PosteriorTotalCentral(),
Total(),
TotalCentral(),
TotalStd(),
Trajectory()
Examples
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")
# Specific time interval ----------------------------------------------------
Med(
phi = phi,
delta_t = 1,
from = "x",
to = "y",
med = "m"
)
# Range of time intervals ---------------------------------------------------
med <- Med(
phi = phi,
delta_t = 1:30,
from = "x",
to = "y",
med = "m"
)
plot(med)
# Methods -------------------------------------------------------------------
# Med has a number of methods including
# print, summary, and plot
med <- Med(
phi = phi,
delta_t = 1:5,
from = "x",
to = "y",
med = "m"
)
print(med)
summary(med)
plot(med)
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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