Standardized Direct Effect of X on Y Over a Specific Time Interval
Source:R/cTMed-direct-std.R
DirectStd.Rd
This function computes the standardized direct effect of the independent variable \(X\) on the dependent variable \(Y\) through mediator variables \(\mathbf{m}\) over a specific time interval \(\Delta t\) using the first-order stochastic differential equation model's drift matrix \(\boldsymbol{\Phi}\) and process noise covariance matrix \(\boldsymbol{\Sigma}\).
Arguments
- phi
Numeric matrix. The drift matrix (\(\boldsymbol{\Phi}\)).
phi
should have row and column names pertaining to the variables in the system.- sigma
Numeric matrix. The process noise covariance matrix (\(\boldsymbol{\Sigma}\)).
- 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
.
Value
Returns an object
of class ctmedeffect
which is a list with the following elements:
- call
Function call.
- args
Function arguments.
- fun
Function used ("DirectStd").
- output
The direct effect.
Details
The standardized direct effect of the independent variable \(X\) on the dependent variable \(Y\) relative to some mediator variables \(\mathbf{m}\) is given by $$ \mathrm{Direct}^{\ast}_{{\Delta t}_{i, j}} = \mathbf{S} \left( \exp \left( \Delta t \mathbf{D} \boldsymbol{\Phi} \mathbf{D} \right)_{i, j} \right) \mathbf{S}^{-1} $$ where \(\boldsymbol{\Phi}\) denotes the drift matrix, \(\mathbf{D}\) a diagonal matrix where the diagonal elements corresponding to mediator variables \(\mathbf{m}\) are set to zero and the rest to one, \(i\) the row index of \(Y\) in \(\boldsymbol{\Phi}\), \(j\) the column index of \(X\) in \(\boldsymbol{\Phi}\), \(\mathbf{S}\) a diagonal matrix with model-implied standard deviations on the diagonals, and \(\Delta t\) the time interval.
References
Bollen, K. A. (1987). Total, direct, and indirect effects in structural equation models. Sociological Methodology, 17, 37. 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. 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. doi:10.1007/s11336-021-09767-0
See also
Other Continuous Time Mediation Functions:
DeltaBeta()
,
DeltaBetaStd()
,
DeltaIndirectCentral()
,
DeltaMed()
,
DeltaMedStd()
,
DeltaTotalCentral()
,
Direct()
,
ExpCov()
,
ExpMean()
,
Indirect()
,
IndirectCentral()
,
IndirectStd()
,
MCBeta()
,
MCBetaStd()
,
MCIndirectCentral()
,
MCMed()
,
MCMedStd()
,
MCPhi()
,
MCTotalCentral()
,
Med()
,
MedStd()
,
PosteriorBeta()
,
PosteriorIndirectCentral()
,
PosteriorMed()
,
PosteriorPhi()
,
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")
sigma <- matrix(
data = c(
0.24455556, 0.02201587, -0.05004762,
0.02201587, 0.07067800, 0.01539456,
-0.05004762, 0.01539456, 0.07553061
),
nrow = 3
)
delta_t <- 1
DirectStd(
phi = phi,
sigma = sigma,
delta_t = delta_t,
from = "x",
to = "y",
med = "m"
)
#> [1] -0.2503