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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

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(), 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
)
#> 
#> Indirect Effect Centrality
#> 
#> $`1`
#>   interval    est     se    R    2.5%  97.5%
#> x        1 0.0005 0.0189 1000 -0.0325 0.0386
#> m        1 0.1667 0.0176 1000  0.1328 0.2023
#> y        1 0.0007 0.0135 1000 -0.0233 0.0277
#> 

# 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)
#> 
#> Indirect Effect Centrality
#> 
#> $`1`
#>   interval    est     se    R    2.5%  97.5%
#> x        1 0.0005 0.0189 1000 -0.0325 0.0386
#> m        1 0.1667 0.0176 1000  0.1328 0.2023
#> y        1 0.0007 0.0135 1000 -0.0233 0.0277
#> 
#> $`2`
#>   interval    est     se    R    2.5%  97.5%
#> x        2 0.0009 0.0370 1000 -0.0670 0.0749
#> m        2 0.3999 0.0465 1000  0.3125 0.4956
#> y        2 0.0015 0.0311 1000 -0.0527 0.0640
#> 
#> $`3`
#>   interval    est     se    R    2.5%  97.5%
#> x        3 0.0005 0.0454 1000 -0.0869 0.0874
#> m        3 0.5431 0.0719 1000  0.4176 0.6970
#> y        3 0.0014 0.0467 1000 -0.0851 0.0936
#> 
#> $`4`
#>   interval     est     se    R    2.5%  97.5%
#> x        4 -0.0001 0.0506 1000 -0.1030 0.0960
#> m        4  0.5864 0.0881 1000  0.4427 0.7814
#> y        4  0.0006 0.0620 1000 -0.1189 0.1163
#> 
#> $`5`
#>   interval     est     se    R    2.5%  97.5%
#> x        5 -0.0003 0.0549 1000 -0.1129 0.1041
#> m        5  0.5598 0.0947 1000  0.4126 0.7809
#> y        5 -0.0004 0.0763 1000 -0.1484 0.1444
#> 
summary(posterior)
#>    variable interval           est         se    R        2.5%      97.5%
#> 1         x        1  5.049093e-04 0.01885505 1000 -0.03250983 0.03857900
#> 2         m        1  1.667085e-01 0.01761895 1000  0.13278798 0.20227734
#> 3         y        1  6.784337e-04 0.01352845 1000 -0.02331382 0.02772267
#> 4         x        2  8.532699e-04 0.03700108 1000 -0.06695886 0.07488156
#> 5         m        2  3.999149e-01 0.04652908 1000  0.31252172 0.49556382
#> 6         y        2  1.468798e-03 0.03108587 1000 -0.05271001 0.06397910
#> 7         x        3  4.856116e-04 0.04536555 1000 -0.08690579 0.08744346
#> 8         m        3  5.431253e-01 0.07185464 1000  0.41756817 0.69698988
#> 9         y        3  1.358015e-03 0.04665813 1000 -0.08512262 0.09356038
#> 10        x        4 -7.646928e-05 0.05056101 1000 -0.10301180 0.09604241
#> 11        m        4  5.863845e-01 0.08811715 1000  0.44270165 0.78135684
#> 12        y        4  5.636874e-04 0.06197609 1000 -0.11892150 0.11625868
#> 13        x        5 -2.802368e-04 0.05492798 1000 -0.11286648 0.10411650
#> 14        m        5  5.597802e-01 0.09472978 1000  0.41257630 0.78088527
#> 15        y        5 -4.203274e-04 0.07632342 1000 -0.14842636 0.14441182
confint(posterior, level = 0.95)
#>    variable interval       2.5 %     97.5 %
#> 1         x        1 -0.03250983 0.03857900
#> 2         m        1  0.13278798 0.20227734
#> 3         y        1 -0.02331382 0.02772267
#> 4         x        2 -0.06695886 0.07488156
#> 5         m        2  0.31252172 0.49556382
#> 6         y        2 -0.05271001 0.06397910
#> 7         x        3 -0.08690579 0.08744346
#> 8         m        3  0.41756817 0.69698988
#> 9         y        3 -0.08512262 0.09356038
#> 10        x        4 -0.10301180 0.09604241
#> 11        m        4  0.44270165 0.78135684
#> 12        y        4 -0.11892150 0.11625868
#> 13        x        5 -0.11286648 0.10411650
#> 14        m        5  0.41257630 0.78088527
#> 15        y        5 -0.14842636 0.14441182
plot(posterior)



#> NULL