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

Source: R/cTMed-posterior-indirect-central.R
PosteriorIndirectCentral.Rd

This function generates a posterior distribution of the 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 \(\boldsymbol{\Phi}\).

Usage

PosteriorIndirectCentral(phi, delta_t, ncores = NULL, tol = 0.01)

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.

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 ("PosteriorIndirectCentral").

output

A list the length of which is equal to the length of delta_t.

Each element in the output list has the following elements:

est

Mean of the posterior distribution of the total, direct, and indirect effects.

thetahatstar

Posterior distribution of the total, direct, and indirect effects.

Details

See TotalCentral() 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(), BootIndirectCentral(), BootMed(), BootMedStd(), BootTotalCentral(), DeltaBeta(), DeltaBetaStd(), DeltaDirectCentral(), DeltaIndirectCentral(), DeltaMed(), DeltaMedStd(), DeltaTotalCentral(), Direct(), DirectCentral(), DirectStd(), Indirect(), IndirectCentral(), IndirectStd(), MCBeta(), MCBetaStd(), MCDirectCentral(), MCIndirectCentral(), MCMed(), MCMedStd(), MCPhi(), MCPhiSigma(), MCTotalCentral(), Med(), MedStd(), PosteriorBeta(), PosteriorDirectCentral(), PosteriorMed(), PosteriorTotalCentral(), Total(), TotalCentral(), TotalStd(), Trajectory()

Author

Ivan Jacob Agaloos Pesigan

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")
vcov_phi_vec <- matrix(
  data = c(
    0.00843, 0.00040, -0.00151,
    -0.00600, -0.00033, 0.00110,
    0.00324, 0.00020, -0.00061,
    0.00040, 0.00374, 0.00016,
    -0.00022, -0.00273, -0.00016,
    0.00009, 0.00150, 0.00012,
    -0.00151, 0.00016, 0.00389,
    0.00103, -0.00007, -0.00283,
    -0.00050, 0.00000, 0.00156,
    -0.00600, -0.00022, 0.00103,
    0.00644, 0.00031, -0.00119,
    -0.00374, -0.00021, 0.00070,
    -0.00033, -0.00273, -0.00007,
    0.00031, 0.00287, 0.00013,
    -0.00014, -0.00170, -0.00012,
    0.00110, -0.00016, -0.00283,
    -0.00119, 0.00013, 0.00297,
    0.00063, -0.00004, -0.00177,
    0.00324, 0.00009, -0.00050,
    -0.00374, -0.00014, 0.00063,
    0.00495, 0.00024, -0.00093,
    0.00020, 0.00150, 0.00000,
    -0.00021, -0.00170, -0.00004,
    0.00024, 0.00214, 0.00012,
    -0.00061, 0.00012, 0.00156,
    0.00070, -0.00012, -0.00177,
    -0.00093, 0.00012, 0.00223
  ),
  nrow = 9
)

phi <- MCPhi(
  phi = phi,
  vcov_phi_vec = vcov_phi_vec,
  R = 1000L
)$output

# Specific time interval ----------------------------------------------------
PosteriorIndirectCentral(
  phi = phi,
  delta_t = 1
)
#> Call:
#> PosteriorIndirectCentral(phi = phi, delta_t = 1)
#> 
#> Indirect Effect Centrality
#>   variable interval    est     se    R    2.5%  97.5%
#> 1        x        1 0.0012 0.0198 1000 -0.0356 0.0386
#> 2        m        1 0.1660 0.0179 1000  0.1336 0.2015
#> 3        y        1 0.0012 0.0139 1000 -0.0256 0.0273

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

# Methods -------------------------------------------------------------------
# PosteriorIndirectCentral has a number of methods including
# print, summary, confint, and plot
print(posterior)
#> Call:
#> PosteriorIndirectCentral(phi = phi, delta_t = 1:5)
#> 
#> Indirect Effect Centrality
#>    variable interval    est     se    R    2.5%  97.5%
#> 1         x        1 0.0012 0.0198 1000 -0.0356 0.0386
#> 2         m        1 0.1660 0.0179 1000  0.1336 0.2015
#> 3         y        1 0.0012 0.0139 1000 -0.0256 0.0273
#> 4         x        2 0.0021 0.0388 1000 -0.0724 0.0724
#> 5         m        2 0.3991 0.0476 1000  0.3140 0.4955
#> 6         y        2 0.0026 0.0320 1000 -0.0565 0.0631
#> 7         x        3 0.0016 0.0471 1000 -0.0909 0.0904
#> 8         m        3 0.5429 0.0737 1000  0.4182 0.7040
#> 9         y        3 0.0028 0.0480 1000 -0.0858 0.0910
#> 10        x        4 0.0007 0.0518 1000 -0.1032 0.1007
#> 11        m        4 0.5868 0.0903 1000  0.4383 0.7983
#> 12        y        4 0.0020 0.0638 1000 -0.1206 0.1184
#> 13        x        5 0.0001 0.0556 1000 -0.1142 0.1062
#> 14        m        5 0.5607 0.0971 1000  0.4051 0.7926
#> 15        y        5 0.0009 0.0787 1000 -0.1532 0.1472
summary(posterior)
#> Call:
#> PosteriorIndirectCentral(phi = phi, delta_t = 1:5)
#> 
#> Indirect Effect Centrality
#>    variable interval    est     se    R    2.5%  97.5%
#> 1         x        1 0.0012 0.0198 1000 -0.0356 0.0386
#> 2         m        1 0.1660 0.0179 1000  0.1336 0.2015
#> 3         y        1 0.0012 0.0139 1000 -0.0256 0.0273
#> 4         x        2 0.0021 0.0388 1000 -0.0724 0.0724
#> 5         m        2 0.3991 0.0476 1000  0.3140 0.4955
#> 6         y        2 0.0026 0.0320 1000 -0.0565 0.0631
#> 7         x        3 0.0016 0.0471 1000 -0.0909 0.0904
#> 8         m        3 0.5429 0.0737 1000  0.4182 0.7040
#> 9         y        3 0.0028 0.0480 1000 -0.0858 0.0910
#> 10        x        4 0.0007 0.0518 1000 -0.1032 0.1007
#> 11        m        4 0.5868 0.0903 1000  0.4383 0.7983
#> 12        y        4 0.0020 0.0638 1000 -0.1206 0.1184
#> 13        x        5 0.0001 0.0556 1000 -0.1142 0.1062
#> 14        m        5 0.5607 0.0971 1000  0.4051 0.7926
#> 15        y        5 0.0009 0.0787 1000 -0.1532 0.1472
confint(posterior, level = 0.95)
#>    variable interval       2.5 %     97.5 %
#> 1         x        1 -0.03562903 0.03858116
#> 2         m        1  0.13355604 0.20146626
#> 3         y        1 -0.02560192 0.02732945
#> 4         x        2 -0.07244090 0.07244703
#> 5         m        2  0.31396819 0.49552641
#> 6         y        2 -0.05645701 0.06313106
#> 7         x        3 -0.09088982 0.09039606
#> 8         m        3  0.41818122 0.70401691
#> 9         y        3 -0.08580920 0.09103733
#> 10        x        4 -0.10316810 0.10071590
#> 11        m        4  0.43826382 0.79833319
#> 12        y        4 -0.12059238 0.11841166
#> 13        x        5 -0.11416462 0.10621817
#> 14        m        5  0.40510439 0.79260397
#> 15        y        5 -0.15315646 0.14723179
plot(posterior)