TotalStd: Standardized Total Effect Matrix Over a Specific Time...

In cTMed: Continuous-Time Mediation

Standardized Total Effect Matrix Over a Specific Time Interval

Description

This function computes the standardized total effects matrix 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

TotalStd(phi, sigma, delta_t)

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).

Details

The standardized total effect matrix over a specific time interval \Delta t is given by

\mathrm{Total}^{\ast}_{{\Delta t}_{i, j}} = \mathrm{Total}_{{\Delta t}_{i, j}} \left( \frac{\sigma_{{x}_{j}}}{\sigma_{{y}_{i}}} \right)

where \boldsymbol{\Phi} denotes the drift matrix, \sigma_{{x}_{j}} and \sigma_{{y}_{i}} are the steady-state model-implied standard deviations of the state independent and dependent variables, respectively, and \Delta t the time interval.

Value

Returns an object of class ctmedeffect which is a list with the following elements:

call

Function call.

args

Function arguments.

fun

Function used ("TotalStd").

output

The standardized matrix of total 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(), Med(), MedStd(), PosteriorBeta(), PosteriorIndirectCentral(), PosteriorMed(), PosteriorTotalCentral(), Total(), TotalCentral(), 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
TotalStd(
  phi = phi,
  sigma = sigma,
  delta_t = delta_t
)

cTMed documentation built on Nov. 5, 2025, 7:18 p.m.