cTMed (version 1.0.6)

TotalStd: Standardized Total Effect Matrix Over a Specific Time Interval

Description

This function computes the standardized total effects matrix over a specific time interval $\mathrm{\Delta }t$ using the first-order stochastic differential equation model's drift matrix $\mathbf{\Phi }$ and process noise covariance matrix $\mathbf{\Sigma }$.

Usage

TotalStd(phi, sigma, delta_t)

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.

Arguments

phi

Numeric matrix. The drift matrix ($\mathbf{\Phi }$). phi should have row and column names pertaining to the variables in the system.

sigma

Numeric matrix. The process noise covariance matrix ($\mathbf{\Sigma }$).

delta_t

Numeric. Time interval ($\mathrm{\Delta }t$).

Author

Ivan Jacob Agaloos Pesigan

Details

The standardized total effect matrix over a specific time interval $\mathrm{\Delta }t$ is given by $${\mathrm{Total}}_{{\mathrm{\Delta }t}_{i,j}}^{\ast }={\mathrm{Total}}_{{\mathrm{\Delta }t}_{i,j}}\left(\frac{{\sigma }_{x_j}}{{\sigma }_{y_i}}\right)$$ where $\mathbf{\Phi }$ 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 $\mathrm{\Delta }t$ 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(), 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
)