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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

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(), 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(), 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"
)
#> 
#> Total, Direct, and Indirect Effects
#> 
#> $`1`
#>          interval     est     se    R    2.5%   97.5%
#> total           1 -0.1009 0.0321 1000 -0.1646 -0.0369
#> direct          1 -0.2672 0.0412 1000 -0.3519 -0.1864
#> indirect        1  0.1664 0.0178 1000  0.1341  0.2019
#> 

# 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)
#> 
#> Total, Direct, and Indirect Effects
#> 
#> $`1`
#>          interval     est     se    R    2.5%   97.5%
#> total           1 -0.1009 0.0321 1000 -0.1646 -0.0369
#> direct          1 -0.2672 0.0412 1000 -0.3519 -0.1864
#> indirect        1  0.1664 0.0178 1000  0.1341  0.2019
#> 
#> $`2`
#>          interval     est     se    R    2.5%   97.5%
#> total           2  0.0771 0.0359 1000  0.0067  0.1431
#> direct          2 -0.3231 0.0588 1000 -0.4503 -0.2173
#> indirect        2  0.4001 0.0476 1000  0.3181  0.4944
#> 
#> $`3`
#>          interval     est     se    R    2.5%   97.5%
#> total           3  0.2477 0.0363 1000  0.1763  0.3161
#> direct          3 -0.2966 0.0659 1000 -0.4448 -0.1861
#> indirect        3  0.5443 0.0737 1000  0.4196  0.7083
#> 
#> $`4`
#>          interval     est     se    R    2.5%   97.5%
#> total           4  0.3429 0.0403 1000  0.2720  0.4240
#> direct          4 -0.2452 0.0669 1000 -0.4024 -0.1399
#> indirect        4  0.5880 0.0905 1000  0.4403  0.7986
#> 
#> $`5`
#>          interval     est     se    R    2.5%   97.5%
#> total           5  0.3688 0.0452 1000  0.2892  0.4669
#> direct          5 -0.1924 0.0639 1000 -0.3493 -0.0978
#> indirect        5  0.5613 0.0974 1000  0.4058  0.7886
#> 
summary(posterior)
#>      effect interval         est         se    R         2.5%       97.5%
#> 1     total        1 -0.10086696 0.03207527 1000 -0.164639300 -0.03693203
#> 2    direct        1 -0.26721948 0.04116205 1000 -0.351915196 -0.18636417
#> 3  indirect        1  0.16635252 0.01783894 1000  0.134057398  0.20187363
#> 4     total        2  0.07708603 0.03591505 1000  0.006701073  0.14307396
#> 5    direct        2 -0.32305468 0.05875878 1000 -0.450341327 -0.21733528
#> 6  indirect        2  0.40014071 0.04758784 1000  0.318069431  0.49442469
#> 7     total        3  0.24767797 0.03634671 1000  0.176293976  0.31605233
#> 8    direct        3 -0.29661770 0.06592929 1000 -0.444837849 -0.18605237
#> 9  indirect        3  0.54429567 0.07372348 1000  0.419642984  0.70832341
#> 10    total        4  0.34285731 0.04027285 1000  0.272023199  0.42401092
#> 11   direct        4 -0.24517689 0.06687169 1000 -0.402406436 -0.13986536
#> 12 indirect        4  0.58803421 0.09050212 1000  0.440284103  0.79855677
#> 13    total        5  0.36884839 0.04521101 1000  0.289211206  0.46693840
#> 14   direct        5 -0.19244653 0.06389833 1000 -0.349267540 -0.09779297
#> 15 indirect        5  0.56129492 0.09736703 1000  0.405791502  0.78861468
confint(posterior, level = 0.95)
#>      effect interval        2.5 %      97.5 %
#> 1     total        1 -0.164639300 -0.03693203
#> 2    direct        1 -0.351915196 -0.18636417
#> 3  indirect        1  0.134057398  0.20187363
#> 4     total        2  0.006701073  0.14307396
#> 5    direct        2 -0.450341327 -0.21733528
#> 6  indirect        2  0.318069431  0.49442469
#> 7     total        3  0.176293976  0.31605233
#> 8    direct        3 -0.444837849 -0.18605237
#> 9  indirect        3  0.419642984  0.70832341
#> 10    total        4  0.272023199  0.42401092
#> 11   direct        4 -0.402406436 -0.13986536
#> 12 indirect        4  0.440284103  0.79855677
#> 13    total        5  0.289211206  0.46693840
#> 14   direct        5 -0.349267540 -0.09779297
#> 15 indirect        5  0.405791502  0.78861468
plot(posterior)