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

Source: R/cTMed-posterior-total-central-std.R
PosteriorTotalCentralStd.Rd

This function generates a posterior distribution of the standardized total 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

PosteriorTotalCentralStd(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 ("PosteriorTotalCentralStd").

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 total effect centrality.

thetahatstar

Posterior distribution of the standardized total effect centrality measure.

Details

See TotalCentralStd() 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(), PosteriorIndirectCentralStd(), PosteriorMed(), PosteriorMedStd(), PosteriorTotalCentral(), 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 ----------------------------------------------------
PosteriorTotalCentralStd(
  phi = phi,
  sigma = sigma,
  delta_t = 1
)
#> Call:
#> PosteriorTotalCentralStd(phi = phi, sigma = sigma, delta_t = 1)
#> 
#> Total Effect Centrality
#>   variable interval    est     se   R    2.5%  97.5%
#> 1        x        1 0.2752 0.0355 100  0.2071 0.3486
#> 2        m        1 0.5588 0.0496 100  0.4572 0.6621
#> 3        y        1 0.0036 0.0283 100 -0.0493 0.0523

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

# Methods -------------------------------------------------------------------
# PosteriorTotalCentralStd has a number of methods including
# print, summary, confint, and plot
print(posterior)
#> Call:
#> PosteriorTotalCentralStd(phi = phi, sigma = sigma, delta_t = 1:5)
#> 
#> Total Effect Centrality
#>    variable interval    est     se   R    2.5%  97.5%
#> 1         x        1 0.2752 0.0355 100  0.2071 0.3486
#> 2         m        1 0.5588 0.0496 100  0.4572 0.6621
#> 3         y        1 0.0036 0.0283 100 -0.0493 0.0523
#> 4         x        2 0.5811 0.0485 100  0.4909 0.6938
#> 5         m        2 0.6187 0.0641 100  0.4846 0.7389
#> 6         y        2 0.0041 0.0395 100 -0.0680 0.0671
#> 7         x        3 0.7533 0.0587 100  0.6582 0.8758
#> 8         m        3 0.5179 0.0717 100  0.3801 0.6571
#> 9         y        3 0.0039 0.0414 100 -0.0684 0.0673
#> 10        x        4 0.7942 0.0685 100  0.6797 0.9256
#> 11        m        4 0.3890 0.0777 100  0.2549 0.5518
#> 12        y        4 0.0036 0.0386 100 -0.0597 0.0625
#> 13        x        5 0.7476 0.0785 100  0.5968 0.8974
#> 14        m        5 0.2772 0.0813 100  0.1426 0.4486
#> 15        y        5 0.0034 0.0337 100 -0.0505 0.0572
summary(posterior)
#> Call:
#> PosteriorTotalCentralStd(phi = phi, sigma = sigma, delta_t = 1:5)
#> 
#> Total Effect Centrality
#>    variable interval    est     se   R    2.5%  97.5%
#> 1         x        1 0.2752 0.0355 100  0.2071 0.3486
#> 2         m        1 0.5588 0.0496 100  0.4572 0.6621
#> 3         y        1 0.0036 0.0283 100 -0.0493 0.0523
#> 4         x        2 0.5811 0.0485 100  0.4909 0.6938
#> 5         m        2 0.6187 0.0641 100  0.4846 0.7389
#> 6         y        2 0.0041 0.0395 100 -0.0680 0.0671
#> 7         x        3 0.7533 0.0587 100  0.6582 0.8758
#> 8         m        3 0.5179 0.0717 100  0.3801 0.6571
#> 9         y        3 0.0039 0.0414 100 -0.0684 0.0673
#> 10        x        4 0.7942 0.0685 100  0.6797 0.9256
#> 11        m        4 0.3890 0.0777 100  0.2549 0.5518
#> 12        y        4 0.0036 0.0386 100 -0.0597 0.0625
#> 13        x        5 0.7476 0.0785 100  0.5968 0.8974
#> 14        m        5 0.2772 0.0813 100  0.1426 0.4486
#> 15        y        5 0.0034 0.0337 100 -0.0505 0.0572
confint(posterior, level = 0.95)
#>    variable interval       2.5 %     97.5 %
#> 1         x        1  0.20707401 0.34862717
#> 2         m        1  0.45718358 0.66207764
#> 3         y        1 -0.04933023 0.05228220
#> 4         x        2  0.49087910 0.69380738
#> 5         m        2  0.48458322 0.73886962
#> 6         y        2 -0.06795443 0.06712097
#> 7         x        3  0.65824293 0.87581426
#> 8         m        3  0.38014063 0.65709191
#> 9         y        3 -0.06843574 0.06733158
#> 10        x        4  0.67969118 0.92564628
#> 11        m        4  0.25492085 0.55177974
#> 12        y        4 -0.05969897 0.06247258
#> 13        x        5  0.59675856 0.89742654
#> 14        m        5  0.14258219 0.44856403
#> 15        y        5 -0.05052143 0.05720078
plot(posterior)