MCMed: Monte Carlo Sampling Distribution of Total, Direct, and...
In cTMed: Continuous Time Mediation
MCMed R Documentation
Monte Carlo Sampling Distribution
of 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 generates a Monte Carlo method
sampling distribution
of 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
drift matrix \boldsymbol{\Phi}.
Usage
MCMed(
phi,
vcov_phi_vec,
delta_t,
from,
to,
med,
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).
delta_t
Numeric.
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.
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
See Total(),
Direct(), and
Indirect() 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 ("MCMed").
- output
A list with length of length(delta_t).
Each element in the output list has the following elements:
- est
A vector of total, direct, and indirect effects.
- thetahatstar
A matrix of Monte Carlo
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:
DeltaBeta(),
DeltaIndirectCentral(),
DeltaMed(),
DeltaTotalCentral(),
Direct(),
Indirect(),
IndirectCentral(),
MCBeta(),
MCIndirectCentral(),
MCPhi(),
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")
vcov_phi_vec <- matrix(
data = c(
0.002704274, -0.001475275, 0.000949122,
-0.001619422, 0.000885122, -0.000569404,
0.00085493, -0.000465824, 0.000297815,
-0.001475275, 0.004428442, -0.002642303,
0.000980573, -0.00271817, 0.001618805,
-0.000586921, 0.001478421, -0.000871547,
0.000949122, -0.002642303, 0.006402668,
-0.000697798, 0.001813471, -0.004043138,
0.000463086, -0.001120949, 0.002271711,
-0.001619422, 0.000980573, -0.000697798,
0.002079286, -0.001152501, 0.000753,
-0.001528701, 0.000820587, -0.000517524,
0.000885122, -0.00271817, 0.001813471,
-0.001152501, 0.00342605, -0.002075005,
0.000899165, -0.002532849, 0.001475579,
-0.000569404, 0.001618805, -0.004043138,
0.000753, -0.002075005, 0.004984032,
-0.000622255, 0.001634917, -0.003705661,
0.00085493, -0.000586921, 0.000463086,
-0.001528701, 0.000899165, -0.000622255,
0.002060076, -0.001096684, 0.000686386,
-0.000465824, 0.001478421, -0.001120949,
0.000820587, -0.002532849, 0.001634917,
-0.001096684, 0.003328692, -0.001926088,
0.000297815, -0.000871547, 0.002271711,
-0.000517524, 0.001475579, -0.003705661,
0.000686386, -0.001926088, 0.004726235
),
nrow = 9
)
# Specific time interval ----------------------------------------------------
MCMed(
phi = phi,
vcov_phi_vec = vcov_phi_vec,
delta_t = 1,
from = "x",
to = "y",
med = "m",
R = 100L # use a large value for R in actual research
)
# Range of time intervals ---------------------------------------------------
mc <- MCMed(
phi = phi,
vcov_phi_vec = vcov_phi_vec,
delta_t = 1:5,
from = "x",
to = "y",
med = "m",
R = 100L # use a large value for R in actual research
)
plot(mc)
# Methods -------------------------------------------------------------------
# MCMed has a number of methods including
# print, summary, confint, and plot
print(mc)
summary(mc)
confint(mc, level = 0.95)
cTMed documentation built on Oct. 21, 2024, 5:08 p.m.
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| MCMed | R Documentation |
Monte Carlo Sampling Distribution of 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 generates a Monte Carlo method
sampling distribution
of 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
drift matrix \boldsymbol{\Phi}.
Usage
MCMed(
phi,
vcov_phi_vec,
delta_t,
from,
to,
med,
R,
test_phi = TRUE,
ncores = NULL,
seed = NULL
)
Arguments
phi |
Numeric matrix.
The drift matrix ( |
vcov_phi_vec |
Numeric matrix.
The sampling variance-covariance matrix of
|
delta_t |
Numeric.
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 |
R |
Positive integer. Number of replications. |
test_phi |
Logical.
If |
ncores |
Positive integer.
Number of cores to use.
If |
seed |
Random seed. |
Details
See Total(),
Direct(), and
Indirect() 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 ("MCMed").
- output
A list with length of
length(delta_t).
Each element in the output list has the following elements:
- est
A vector of total, direct, and indirect effects.
- thetahatstar
A matrix of Monte Carlo 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:
DeltaBeta(),
DeltaIndirectCentral(),
DeltaMed(),
DeltaTotalCentral(),
Direct(),
Indirect(),
IndirectCentral(),
MCBeta(),
MCIndirectCentral(),
MCPhi(),
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")
vcov_phi_vec <- matrix(
data = c(
0.002704274, -0.001475275, 0.000949122,
-0.001619422, 0.000885122, -0.000569404,
0.00085493, -0.000465824, 0.000297815,
-0.001475275, 0.004428442, -0.002642303,
0.000980573, -0.00271817, 0.001618805,
-0.000586921, 0.001478421, -0.000871547,
0.000949122, -0.002642303, 0.006402668,
-0.000697798, 0.001813471, -0.004043138,
0.000463086, -0.001120949, 0.002271711,
-0.001619422, 0.000980573, -0.000697798,
0.002079286, -0.001152501, 0.000753,
-0.001528701, 0.000820587, -0.000517524,
0.000885122, -0.00271817, 0.001813471,
-0.001152501, 0.00342605, -0.002075005,
0.000899165, -0.002532849, 0.001475579,
-0.000569404, 0.001618805, -0.004043138,
0.000753, -0.002075005, 0.004984032,
-0.000622255, 0.001634917, -0.003705661,
0.00085493, -0.000586921, 0.000463086,
-0.001528701, 0.000899165, -0.000622255,
0.002060076, -0.001096684, 0.000686386,
-0.000465824, 0.001478421, -0.001120949,
0.000820587, -0.002532849, 0.001634917,
-0.001096684, 0.003328692, -0.001926088,
0.000297815, -0.000871547, 0.002271711,
-0.000517524, 0.001475579, -0.003705661,
0.000686386, -0.001926088, 0.004726235
),
nrow = 9
)
# Specific time interval ----------------------------------------------------
MCMed(
phi = phi,
vcov_phi_vec = vcov_phi_vec,
delta_t = 1,
from = "x",
to = "y",
med = "m",
R = 100L # use a large value for R in actual research
)
# Range of time intervals ---------------------------------------------------
mc <- MCMed(
phi = phi,
vcov_phi_vec = vcov_phi_vec,
delta_t = 1:5,
from = "x",
to = "y",
med = "m",
R = 100L # use a large value for R in actual research
)
plot(mc)
# Methods -------------------------------------------------------------------
# MCMed has a number of methods including
# print, summary, confint, and plot
print(mc)
summary(mc)
confint(mc, level = 0.95)
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