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.RdThis 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 \(\boldsymbol{\Phi}\).
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 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 ("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()
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 -0.0998 0.0307 1000 -0.1665 -0.0426
#> direct 1 -0.2664 0.0395 1000 -0.3488 -0.1949
#> indirect 1 0.1666 0.0175 1000 0.1345 0.2033
#>
# 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 -0.0998 0.0307 1000 -0.1665 -0.0426
#> direct 1 -0.2664 0.0395 1000 -0.3488 -0.1949
#> indirect 1 0.1666 0.0175 1000 0.1345 0.2033
#>
#> $`2`
#> interval est se R 2.5% 97.5%
#> total 2 0.0791 0.0343 1000 0.0044 0.1380
#> direct 2 -0.3209 0.0564 1000 -0.4448 -0.2203
#> indirect 2 0.4000 0.0465 1000 0.3159 0.4971
#>
#> $`3`
#> interval est se R 2.5% 97.5%
#> total 3 0.2497 0.0350 1000 0.1816 0.3176
#> direct 3 -0.2937 0.0637 1000 -0.4384 -0.1875
#> indirect 3 0.5433 0.0723 1000 0.4154 0.6986
#>
#> $`4`
#> interval est se R 2.5% 97.5%
#> total 4 0.3442 0.0393 1000 0.2728 0.4219
#> direct 4 -0.2419 0.0649 1000 -0.3952 -0.1405
#> indirect 4 0.5862 0.0890 1000 0.4338 0.7824
#>
#> $`5`
#> interval est se R 2.5% 97.5%
#> total 5 0.3695 0.0444 1000 0.2879 0.4614
#> direct 5 -0.1893 0.0622 1000 -0.3465 -0.0973
#> indirect 5 0.5588 0.0958 1000 0.4051 0.7721
#>
summary(posterior)
#> effect interval est se R 2.5% 97.5%
#> 1 total 1 -0.09982408 0.03072857 1000 -0.166470645 -0.04260420
#> 2 direct 1 -0.26638884 0.03950558 1000 -0.348803573 -0.19489083
#> 3 indirect 1 0.16656476 0.01746824 1000 0.134503056 0.20333979
#> 4 total 2 0.07907750 0.03431010 1000 0.004369168 0.13802573
#> 5 direct 2 -0.32091784 0.05643154 1000 -0.444768981 -0.22030376
#> 6 indirect 2 0.39999534 0.04654189 1000 0.315851481 0.49710561
#> 7 total 3 0.24965142 0.03501717 1000 0.181639312 0.31755141
#> 8 direct 3 -0.29366589 0.06366600 1000 -0.438396767 -0.18748070
#> 9 indirect 3 0.54331732 0.07229832 1000 0.415430083 0.69859417
#> 10 total 4 0.34424742 0.03930801 1000 0.272760335 0.42191848
#> 11 direct 4 -0.24194907 0.06488365 1000 -0.395163282 -0.14053097
#> 12 indirect 4 0.58619649 0.08897487 1000 0.433771997 0.78244742
#> 13 total 5 0.36949024 0.04440278 1000 0.287872340 0.46141766
#> 14 direct 5 -0.18930907 0.06218313 1000 -0.346457942 -0.09726921
#> 15 indirect 5 0.55879932 0.09583415 1000 0.405107599 0.77212881
confint(posterior, level = 0.95)
#> effect interval 2.5 % 97.5 %
#> 1 total 1 -0.166470645 -0.04260420
#> 2 direct 1 -0.348803573 -0.19489083
#> 3 indirect 1 0.134503056 0.20333979
#> 4 total 2 0.004369168 0.13802573
#> 5 direct 2 -0.444768981 -0.22030376
#> 6 indirect 2 0.315851481 0.49710561
#> 7 total 3 0.181639312 0.31755141
#> 8 direct 3 -0.438396767 -0.18748070
#> 9 indirect 3 0.415430083 0.69859417
#> 10 total 4 0.272760335 0.42191848
#> 11 direct 4 -0.395163282 -0.14053097
#> 12 indirect 4 0.433771997 0.78244742
#> 13 total 5 0.287872340 0.46141766
#> 14 direct 5 -0.346457942 -0.09726921
#> 15 indirect 5 0.405107599 0.77212881
plot(posterior)
#> NULL