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Posterior Distribution of Total, Direct, and Indirect Effects of X on Y Through M Over a Specific Time Interval or a Range of Time Intervals

Source: R/cTMed-posterior-med.R
PosteriorMed.Rd

This function generates a posterior distribution of the total, direct and indirect effects of the independent variable \(X\) on the dependent variable \(Y\) through mediator variables \(\mathbf{m}\) 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

PosteriorMed(phi, delta_t, from, to, med, 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 (\(\Delta t\)).

from

Character string. Name of the independent variable \(X\) in phi.

to

Character string. Name of the dependent variable \(Y\) in phi.

med

Character vector. Name/s of the mediator variable/s in phi.

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 ("PosteriorMed").

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 Total(), Direct(), and Indirect() 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(), PosteriorIndirectCentral(), 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 ----------------------------------------------------
PosteriorMed(
  phi = phi,
  delta_t = 1,
  from = "x",
  to = "y",
  med = "m"
)
#> Call:
#> PosteriorMed(phi = phi, delta_t = 1, from = "x", to = "y", med = "m")
#> 
#> Total, Direct, and Indirect Effects
#> 
#>     effect interval     est     se    R    2.5%   97.5%
#> 1    total        1 -0.0998 0.0300 1000 -0.1541 -0.0428
#> 2   direct        1 -0.2681 0.0394 1000 -0.3443 -0.1939
#> 3 indirect        1  0.1683 0.0178 1000  0.1340  0.2037

# Range of time intervals ---------------------------------------------------
posterior <- PosteriorMed(
  phi = phi,
  delta_t = 1:5,
  from = "x",
  to = "y",
  med = "m"
)

# Methods -------------------------------------------------------------------
# PosteriorMed has a number of methods including
# print, summary, confint, and plot
print(posterior)
#> Call:
#> PosteriorMed(phi = phi, delta_t = 1:5, from = "x", to = "y", 
#>     med = "m")
#> 
#> Total, Direct, and Indirect Effects
#> 
#>      effect interval     est     se    R    2.5%   97.5%
#> 1     total        1 -0.0998 0.0300 1000 -0.1541 -0.0428
#> 2    direct        1 -0.2681 0.0394 1000 -0.3443 -0.1939
#> 3  indirect        1  0.1683 0.0178 1000  0.1340  0.2037
#> 4     total        2  0.0802 0.0329 1000  0.0145  0.1446
#> 5    direct        2 -0.3231 0.0560 1000 -0.4327 -0.2247
#> 6  indirect        2  0.4033 0.0472 1000  0.3157  0.5009
#> 7     total        3  0.2515 0.0342 1000  0.1849  0.3216
#> 8    direct        3 -0.2957 0.0626 1000 -0.4238 -0.1898
#> 9  indirect        3  0.5471 0.0728 1000  0.4195  0.7048
#> 10    total        4  0.3465 0.0393 1000  0.2786  0.4346
#> 11   direct        4 -0.2436 0.0633 1000 -0.3827 -0.1413
#> 12 indirect        4  0.5901 0.0889 1000  0.4436  0.7843
#> 13    total        5  0.3722 0.0446 1000  0.2983  0.4719
#> 14   direct        5 -0.1906 0.0603 1000 -0.3309 -0.1006
#> 15 indirect        5  0.5628 0.0951 1000  0.4087  0.7885
summary(posterior)
#> Call:
#> PosteriorMed(phi = phi, delta_t = 1:5, from = "x", to = "y", 
#>     med = "m")
#> 
#> Total, Direct, and Indirect Effects
#> 
#>      effect interval     est     se    R    2.5%   97.5%
#> 1     total        1 -0.0998 0.0300 1000 -0.1541 -0.0428
#> 2    direct        1 -0.2681 0.0394 1000 -0.3443 -0.1939
#> 3  indirect        1  0.1683 0.0178 1000  0.1340  0.2037
#> 4     total        2  0.0802 0.0329 1000  0.0145  0.1446
#> 5    direct        2 -0.3231 0.0560 1000 -0.4327 -0.2247
#> 6  indirect        2  0.4033 0.0472 1000  0.3157  0.5009
#> 7     total        3  0.2515 0.0342 1000  0.1849  0.3216
#> 8    direct        3 -0.2957 0.0626 1000 -0.4238 -0.1898
#> 9  indirect        3  0.5471 0.0728 1000  0.4195  0.7048
#> 10    total        4  0.3465 0.0393 1000  0.2786  0.4346
#> 11   direct        4 -0.2436 0.0633 1000 -0.3827 -0.1413
#> 12 indirect        4  0.5901 0.0889 1000  0.4436  0.7843
#> 13    total        5  0.3722 0.0446 1000  0.2983  0.4719
#> 14   direct        5 -0.1906 0.0603 1000 -0.3309 -0.1006
#> 15 indirect        5  0.5628 0.0951 1000  0.4087  0.7885
confint(posterior, level = 0.95)
#>      effect interval      2.5 %      97.5 %
#> 1     total        1 -0.1541331 -0.04278507
#> 2    direct        1 -0.3442722 -0.19389771
#> 3  indirect        1  0.1339817  0.20369213
#> 4     total        2  0.0145340  0.14459580
#> 5    direct        2 -0.4326701 -0.22470431
#> 6  indirect        2  0.3157411  0.50092997
#> 7     total        3  0.1849007  0.32164073
#> 8    direct        3 -0.4237842 -0.18982649
#> 9  indirect        3  0.4194591  0.70481461
#> 10    total        4  0.2786364  0.43455167
#> 11   direct        4 -0.3827311 -0.14134158
#> 12 indirect        4  0.4436055  0.78428773
#> 13    total        5  0.2983093  0.47189128
#> 14   direct        5 -0.3308675 -0.10056713
#> 15 indirect        5  0.4086515  0.78851620
plot(posterior)