cTMed (version 1.0.4)

DirectStd: Standardized Direct Effect of X on Y Over a Specific Time Interval

Description

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 \(\boldsymbol{\Sigma}\).

Usage

DirectStd(phi, sigma, delta_t, from, to, med)

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 standardized direct effect.

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.

Author

Ivan Jacob Agaloos Pesigan

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. 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. 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. tools:::Rd_expr_doi("10.1007/s11336-021-09767-0")

See Also

Other Continuous Time Mediation Functions: BootBeta(), BootBetaStd(), BootMed(), BootMedStd(), DeltaBeta(), DeltaBetaStd(), DeltaIndirectCentral(), DeltaMed(), DeltaMedStd(), DeltaTotalCentral(), Direct(), ExpCov(), ExpMean(), Indirect(), IndirectCentral(), IndirectStd(), MCBeta(), MCBetaStd(), MCIndirectCentral(), MCMed(), MCMedStd(), MCPhi(), MCTotalCentral(), Med(), 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")
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"
)