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Posterior Distribution of the Standardized Indirect Effect Centrality Over a Specific Time Interval or a Range of Time Intervals

Source: R/cTMed-posterior-indirect-central-std.R
PosteriorIndirectCentralStd.Rd

This function generates a posterior distribution of the standardized indirect effect centrality over a specific time interval \(\Delta t\) or a range of time intervals using the posterior distribution of the first-order stochastic differential equation model drift matrix \(\boldsymbol{\Phi}\) and process noise covariance matrix \(\boldsymbol{\Sigma}\).

Usage

PosteriorIndirectCentralStd(phi, sigma, delta_t, ncores = NULL, tol = 0.001)

Arguments

phi

List of numeric matrices. Each element of the list is a sample from the posterior distribution of the drift matrix (\(\boldsymbol{\Phi}\)). Each matrix should have row and column names pertaining to the variables in the system.

sigma

List of numeric matrices. Each element is a posterior draw of the diffusion covariance matrix.

delta_t

Numeric. Time interval (\(\Delta t\)).

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.

tol

Numeric. Smallest possible time interval to allow.

Value

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

call

Function call.

args

Function arguments.

fun

Function used ("PosteriorIndirectCentralStd").

output

A list of length length(delta_t).

Each element in the output list has the following elements:

est

Mean of the posterior distribution of the standardized indirect effect centrality.

thetahatstar

Posterior distribution of the standardized indirect effect centrality measure.

Details

See IndirectCentralStd() for more details.

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

Pesigan, I. J. A., Russell, M. A., & Chow, S.-M. (2025). Inferences and effect sizes for direct, indirect, and total effects in continuous-time mediation models. Psychological Methods. doi:10.1037/met0000779

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: BootBeta(), BootBetaStd(), BootDirectCentral(), BootDirectCentralStd(), BootIndirectCentral(), BootIndirectCentralStd(), BootMed(), BootMedStd(), BootTotalCentral(), BootTotalCentralStd(), DeltaBeta(), DeltaBetaStd(), DeltaDirectCentral(), DeltaDirectCentralStd(), DeltaIndirectCentral(), DeltaMed(), DeltaMedStd(), DeltaTotalCentral(), DeltaTotalCentralStd(), Direct(), DirectCentral(), DirectCentralStd(), DirectStd(), Indirect(), IndirectCentral(), IndirectCentralStd(), IndirectStd(), MCBeta(), MCBetaStd(), MCDirectCentral(), MCDirectCentralStd(), MCIndirectCentral(), MCIndirectCentralStd(), MCMed(), MCMedStd(), MCPhi(), MCPhiSigma(), MCTotalCentral(), MCTotalCentralStd(), Med(), MedStd(), PosteriorBeta(), PosteriorBetaStd(), PosteriorDirectCentral(), PosteriorDirectCentralStd(), PosteriorIndirectCentral(), PosteriorMed(), PosteriorMedStd(), PosteriorTotalCentral(), PosteriorTotalCentralStd(), Total(), TotalCentral(), TotalCentralStd(), TotalStd(), Trajectory()

Author

Ivan Jacob Agaloos Pesigan

Examples

set.seed(42)
phi <- matrix(
  data = c(
    -0.357, 0.771, -0.450,
    0.000, -0.511, 0.729,
    0.000, 0.000, -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
)
colnames(sigma) <- rownames(sigma) <- c("x", "m", "y")

input <- MCPhiSigma(
  phi = phi,
  sigma = sigma,
  vcov_theta = 0.001 * diag(15),
  R = 100L,
  seed = 42
)$output

phi <- lapply(
  X = input,
  FUN = function(x) {
    x[[1]]
  }
)

sigma <- lapply(
  X = input,
  FUN = function(x) {
    x[[2]]
  }
)

# Specific time interval ----------------------------------------------------
PosteriorIndirectCentralStd(
  phi = phi,
  sigma = sigma,
  delta_t = 1
)
#> Call:
#> PosteriorIndirectCentralStd(phi = phi, sigma = sigma, delta_t = 1)
#> 
#> Indirect Effect Centrality
#>   variable interval     est     se   R    2.5%  97.5%
#> 1        x        1 -0.0006 0.0049 100 -0.0100 0.0087
#> 2        m        1  0.1781 0.0191 100  0.1452 0.2131
#> 3        y        1 -0.0003 0.0089 100 -0.0167 0.0151

# Range of time intervals ---------------------------------------------------
posterior <- PosteriorIndirectCentralStd(
  phi = phi,
  sigma = sigma,
  delta_t = 1:5
)

# Methods -------------------------------------------------------------------
# PosteriorIndirectCentralStd has a number of methods including
# print, summary, confint, and plot
print(posterior)
#> Call:
#> PosteriorIndirectCentralStd(phi = phi, sigma = sigma, delta_t = 1:5)
#> 
#> Indirect Effect Centrality
#>    variable interval     est     se   R    2.5%  97.5%
#> 1         x        1 -0.0006 0.0049 100 -0.0100 0.0087
#> 2         m        1  0.1781 0.0191 100  0.1452 0.2131
#> 3         y        1 -0.0003 0.0089 100 -0.0167 0.0151
#> 4         x        2 -0.0005 0.0106 100 -0.0198 0.0161
#> 5         m        2  0.4260 0.0458 100  0.3531 0.5071
#> 6         y        2  0.0000 0.0208 100 -0.0379 0.0319
#> 7         x        3  0.0006 0.0192 100 -0.0355 0.0307
#> 8         m        3  0.5768 0.0639 100  0.4832 0.6934
#> 9         y        3  0.0011 0.0301 100 -0.0520 0.0463
#> 10        x        4  0.0023 0.0304 100 -0.0543 0.0557
#> 11        m        4  0.6212 0.0727 100  0.5111 0.7563
#> 12        y        4  0.0025 0.0373 100 -0.0645 0.0608
#> 13        x        5  0.0040 0.0408 100 -0.0715 0.0788
#> 14        m        5  0.5920 0.0749 100  0.4804 0.7388
#> 15        y        5  0.0038 0.0428 100 -0.0727 0.0732
summary(posterior)
#> Call:
#> PosteriorIndirectCentralStd(phi = phi, sigma = sigma, delta_t = 1:5)
#> 
#> Indirect Effect Centrality
#>    variable interval     est     se   R    2.5%  97.5%
#> 1         x        1 -0.0006 0.0049 100 -0.0100 0.0087
#> 2         m        1  0.1781 0.0191 100  0.1452 0.2131
#> 3         y        1 -0.0003 0.0089 100 -0.0167 0.0151
#> 4         x        2 -0.0005 0.0106 100 -0.0198 0.0161
#> 5         m        2  0.4260 0.0458 100  0.3531 0.5071
#> 6         y        2  0.0000 0.0208 100 -0.0379 0.0319
#> 7         x        3  0.0006 0.0192 100 -0.0355 0.0307
#> 8         m        3  0.5768 0.0639 100  0.4832 0.6934
#> 9         y        3  0.0011 0.0301 100 -0.0520 0.0463
#> 10        x        4  0.0023 0.0304 100 -0.0543 0.0557
#> 11        m        4  0.6212 0.0727 100  0.5111 0.7563
#> 12        y        4  0.0025 0.0373 100 -0.0645 0.0608
#> 13        x        5  0.0040 0.0408 100 -0.0715 0.0788
#> 14        m        5  0.5920 0.0749 100  0.4804 0.7388
#> 15        y        5  0.0038 0.0428 100 -0.0727 0.0732
confint(posterior, level = 0.95)
#>    variable interval        2.5 %      97.5 %
#> 1         x        1 -0.009991491 0.008712481
#> 2         m        1  0.145235035 0.213100578
#> 3         y        1 -0.016687532 0.015126158
#> 4         x        2 -0.019842453 0.016098764
#> 5         m        2  0.353137765 0.507054970
#> 6         y        2 -0.037873960 0.031930954
#> 7         x        3 -0.035536661 0.030662054
#> 8         m        3  0.483240371 0.693426107
#> 9         y        3 -0.052022732 0.046317996
#> 10        x        4 -0.054342499 0.055743710
#> 11        m        4  0.511107527 0.756309068
#> 12        y        4 -0.064527324 0.060787523
#> 13        x        5 -0.071513516 0.078787667
#> 14        m        5  0.480385059 0.738783716
#> 15        y        5 -0.072699808 0.073208181
plot(posterior)