Posterior Sampling Distribution for the Elements of the Matrix of Lagged Coefficients Over a Specific Time Interval or a Range of Time Intervals
Source:R/cTMed-posterior-beta.R
PosteriorBeta.RdThis function generates a posterior sampling distribution for the elements of the matrix of lagged coefficients \(\boldsymbol{\beta}\) over a specific time interval \(\Delta t\) or a range of time intervals using the first-order stochastic differential equation model drift matrix \(\boldsymbol{\Phi}\).
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 replicationsRis 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 ("PosteriorBeta").
- 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
A vector of total, direct, and indirect effects.
- thetahatstar
A matrix of Monte Carlo total, direct, and indirect effects.
Details
See Total().
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(),
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(),
PosteriorIndirectCentral(),
PosteriorMed(),
PosteriorTotalCentral(),
Total(),
TotalCentral(),
TotalStd(),
Trajectory()
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 ----------------------------------------------------
PosteriorBeta(
phi = phi,
delta_t = 1
)
#> Call:
#> PosteriorBeta(phi = phi, delta_t = 1)
#>
#> Total, Direct, and Indirect Effects
#>
#> effect interval est se R 2.5% 97.5%
#> 1 from x to x 1 0.7007 0.0488 1000 0.6088 0.8038
#> 2 from x to m 1 0.5022 0.0351 1000 0.4361 0.5713
#> 3 from x to y 1 -0.1011 0.0318 1000 -0.1678 -0.0433
#> 4 from m to x 1 -0.0001 0.0440 1000 -0.0901 0.0794
#> 5 from m to m 1 0.5999 0.0332 1000 0.5334 0.6655
#> 6 from m to y 1 0.4008 0.0282 1000 0.3472 0.4588
#> 7 from y to x 1 0.0001 0.0402 1000 -0.0801 0.0798
#> 8 from y to m 1 0.0007 0.0319 1000 -0.0637 0.0631
#> 9 from y to y 1 0.4995 0.0277 1000 0.4446 0.5535
# Range of time intervals ---------------------------------------------------
posterior <- PosteriorBeta(
phi = phi,
delta_t = 1:5
)
plot(posterior)
# Methods -------------------------------------------------------------------
# PosteriorBeta has a number of methods including
# print, summary, confint, and plot
print(posterior)
#> Call:
#> PosteriorBeta(phi = phi, delta_t = 1:5)
#>
#> Total, Direct, and Indirect Effects
#>
#> effect interval est se R 2.5% 97.5%
#> 1 from x to x 1 0.7007 0.0488 1000 0.6088 0.8038
#> 2 from x to m 1 0.5022 0.0351 1000 0.4361 0.5713
#> 3 from x to y 1 -0.1011 0.0318 1000 -0.1678 -0.0433
#> 4 from m to x 1 -0.0001 0.0440 1000 -0.0901 0.0794
#> 5 from m to m 1 0.5999 0.0332 1000 0.5334 0.6655
#> 6 from m to y 1 0.4008 0.0282 1000 0.3472 0.4588
#> 7 from y to x 1 0.0001 0.0402 1000 -0.0801 0.0798
#> 8 from y to m 1 0.0007 0.0319 1000 -0.0637 0.0631
#> 9 from y to y 1 0.4995 0.0277 1000 0.4446 0.5535
#> 10 from x to x 2 0.4909 0.0572 1000 0.3899 0.6175
#> 11 from x to m 2 0.6530 0.0545 1000 0.5520 0.7660
#> 12 from x to y 2 0.0799 0.0348 1000 0.0074 0.1436
#> 13 from m to x 2 -0.0001 0.0531 1000 -0.1129 0.0945
#> 14 from m to m 2 0.3601 0.0517 1000 0.2555 0.4611
#> 15 from m to y 2 0.4407 0.0325 1000 0.3817 0.5102
#> 16 from y to x 2 0.0001 0.0484 1000 -0.0963 0.0965
#> 17 from y to m 2 0.0008 0.0494 1000 -0.1009 0.0992
#> 18 from y to y 2 0.2498 0.0327 1000 0.1846 0.3119
#> 19 from x to x 3 0.3439 0.0568 1000 0.2462 0.4674
#> 20 from x to m 3 0.6383 0.0673 1000 0.5159 0.7808
#> 21 from x to y 3 0.2521 0.0343 1000 0.1835 0.3203
#> 22 from m to x 3 -0.0001 0.0521 1000 -0.1111 0.0953
#> 23 from m to m 3 0.2162 0.0635 1000 0.0864 0.3347
#> 24 from m to y 3 0.3645 0.0329 1000 0.3076 0.4421
#> 25 from y to x 3 0.0001 0.0443 1000 -0.0899 0.0867
#> 26 from y to m 3 0.0007 0.0581 1000 -0.1192 0.1182
#> 27 from y to y 3 0.1251 0.0311 1000 0.0667 0.1868
#> 28 from x to x 4 0.2409 0.0554 1000 0.1459 0.3639
#> 29 from x to m 4 0.5558 0.0741 1000 0.4306 0.7278
#> 30 from x to y 4 0.3470 0.0383 1000 0.2738 0.4232
#> 31 from m to x 4 -0.0001 0.0479 1000 -0.0995 0.0879
#> 32 from m to m 4 0.1299 0.0686 1000 -0.0070 0.2599
#> 33 from m to y 4 0.2688 0.0361 1000 0.2035 0.3518
#> 34 from y to x 4 0.0000 0.0365 1000 -0.0735 0.0694
#> 35 from y to m 4 0.0005 0.0591 1000 -0.1193 0.1187
#> 36 from y to y 4 0.0628 0.0318 1000 0.0034 0.1238
#> 37 from x to x 5 0.1688 0.0546 1000 0.0729 0.2879
#> 38 from x to m 5 0.4546 0.0774 1000 0.3254 0.6292
#> 39 from x to y 5 0.3718 0.0438 1000 0.2943 0.4644
#> 40 from m to x 5 -0.0001 0.0422 1000 -0.0815 0.0809
#> 41 from m to m 5 0.0781 0.0685 1000 -0.0525 0.2114
#> 42 from m to y 5 0.1863 0.0400 1000 0.1114 0.2737
#> 43 from y to x 5 0.0000 0.0286 1000 -0.0569 0.0575
#> 44 from y to m 5 0.0004 0.0549 1000 -0.1088 0.1073
#> 45 from y to y 5 0.0316 0.0342 1000 -0.0346 0.1011
summary(posterior)
#> Call:
#> PosteriorBeta(phi = phi, delta_t = 1:5)
#>
#> Total, Direct, and Indirect Effects
#>
#> effect interval est se R 2.5% 97.5%
#> 1 from x to x 1 0.7007 0.0488 1000 0.6088 0.8038
#> 2 from x to m 1 0.5022 0.0351 1000 0.4361 0.5713
#> 3 from x to y 1 -0.1011 0.0318 1000 -0.1678 -0.0433
#> 4 from m to x 1 -0.0001 0.0440 1000 -0.0901 0.0794
#> 5 from m to m 1 0.5999 0.0332 1000 0.5334 0.6655
#> 6 from m to y 1 0.4008 0.0282 1000 0.3472 0.4588
#> 7 from y to x 1 0.0001 0.0402 1000 -0.0801 0.0798
#> 8 from y to m 1 0.0007 0.0319 1000 -0.0637 0.0631
#> 9 from y to y 1 0.4995 0.0277 1000 0.4446 0.5535
#> 10 from x to x 2 0.4909 0.0572 1000 0.3899 0.6175
#> 11 from x to m 2 0.6530 0.0545 1000 0.5520 0.7660
#> 12 from x to y 2 0.0799 0.0348 1000 0.0074 0.1436
#> 13 from m to x 2 -0.0001 0.0531 1000 -0.1129 0.0945
#> 14 from m to m 2 0.3601 0.0517 1000 0.2555 0.4611
#> 15 from m to y 2 0.4407 0.0325 1000 0.3817 0.5102
#> 16 from y to x 2 0.0001 0.0484 1000 -0.0963 0.0965
#> 17 from y to m 2 0.0008 0.0494 1000 -0.1009 0.0992
#> 18 from y to y 2 0.2498 0.0327 1000 0.1846 0.3119
#> 19 from x to x 3 0.3439 0.0568 1000 0.2462 0.4674
#> 20 from x to m 3 0.6383 0.0673 1000 0.5159 0.7808
#> 21 from x to y 3 0.2521 0.0343 1000 0.1835 0.3203
#> 22 from m to x 3 -0.0001 0.0521 1000 -0.1111 0.0953
#> 23 from m to m 3 0.2162 0.0635 1000 0.0864 0.3347
#> 24 from m to y 3 0.3645 0.0329 1000 0.3076 0.4421
#> 25 from y to x 3 0.0001 0.0443 1000 -0.0899 0.0867
#> 26 from y to m 3 0.0007 0.0581 1000 -0.1192 0.1182
#> 27 from y to y 3 0.1251 0.0311 1000 0.0667 0.1868
#> 28 from x to x 4 0.2409 0.0554 1000 0.1459 0.3639
#> 29 from x to m 4 0.5558 0.0741 1000 0.4306 0.7278
#> 30 from x to y 4 0.3470 0.0383 1000 0.2738 0.4232
#> 31 from m to x 4 -0.0001 0.0479 1000 -0.0995 0.0879
#> 32 from m to m 4 0.1299 0.0686 1000 -0.0070 0.2599
#> 33 from m to y 4 0.2688 0.0361 1000 0.2035 0.3518
#> 34 from y to x 4 0.0000 0.0365 1000 -0.0735 0.0694
#> 35 from y to m 4 0.0005 0.0591 1000 -0.1193 0.1187
#> 36 from y to y 4 0.0628 0.0318 1000 0.0034 0.1238
#> 37 from x to x 5 0.1688 0.0546 1000 0.0729 0.2879
#> 38 from x to m 5 0.4546 0.0774 1000 0.3254 0.6292
#> 39 from x to y 5 0.3718 0.0438 1000 0.2943 0.4644
#> 40 from m to x 5 -0.0001 0.0422 1000 -0.0815 0.0809
#> 41 from m to m 5 0.0781 0.0685 1000 -0.0525 0.2114
#> 42 from m to y 5 0.1863 0.0400 1000 0.1114 0.2737
#> 43 from y to x 5 0.0000 0.0286 1000 -0.0569 0.0575
#> 44 from y to m 5 0.0004 0.0549 1000 -0.1088 0.1073
#> 45 from y to y 5 0.0316 0.0342 1000 -0.0346 0.1011
confint(posterior, level = 0.95)
#> effect interval 2.5 % 97.5 %
#> 1 from x to x 1 0.608787051 0.80378813
#> 2 from x to m 1 0.436064479 0.57132115
#> 3 from x to y 1 -0.167796773 -0.04326155
#> 4 from x to x 2 0.389924244 0.61745605
#> 5 from x to m 2 0.552019346 0.76595378
#> 6 from x to y 2 0.007428498 0.14362689
#> 7 from x to x 3 0.246244665 0.46744703
#> 8 from x to m 3 0.515931515 0.78083560
#> 9 from x to y 3 0.183482045 0.32030654
#> 10 from x to x 4 0.145868037 0.36392793
#> 11 from x to m 4 0.430579036 0.72776025
#> 12 from x to y 4 0.273844483 0.42324830
#> 13 from x to x 5 0.072856859 0.28794674
#> 14 from x to m 5 0.325389617 0.62922260
#> 15 from x to y 5 0.294271102 0.46444840
plot(posterior)
