Bootstrap 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-boot-beta.R
BootBeta.RdThis function generates a bootstrap method 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 bootstrap estimate of the drift matrix (\(\boldsymbol{\Phi}\)).
- phi_hat
Numeric matrix. The estimated drift matrix (\(\hat{\boldsymbol{\Phi}}\)) from the original data set.
phi_hatshould 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 ctmedboot which is a list with the following elements:
- call
Function call.
- args
Function arguments.
- fun
Function used ("BootBeta").
- output
A list with length of
length(delta_t).
Each element in the output list has the following elements:
- est
Estimated elements of the matrix of lagged coefficients.
- thetahatstar
A matrix of bootstrap elements of the matrix of lagged coefficients.
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
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:
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(),
PosteriorMed(),
PosteriorTotalCentral(),
Total(),
TotalCentral(),
TotalStd(),
Trajectory()
Examples
# \donttest{
library(bootStateSpace)
# prepare parameters
## number of individuals
n <- 50
## time points
time <- 100
delta_t <- 0.10
## dynamic structure
p <- 3
mu0 <- rep(x = 0, times = p)
sigma0 <- matrix(
data = c(
1.0,
0.2,
0.2,
0.2,
1.0,
0.2,
0.2,
0.2,
1.0
),
nrow = p
)
sigma0_l <- t(chol(sigma0))
mu <- rep(x = 0, times = p)
phi <- matrix(
data = c(
-0.357,
0.771,
-0.450,
0.0,
-0.511,
0.729,
0,
0,
-0.693
),
nrow = p
)
sigma <- matrix(
data = c(
0.24455556,
0.02201587,
-0.05004762,
0.02201587,
0.07067800,
0.01539456,
-0.05004762,
0.01539456,
0.07553061
),
nrow = p
)
sigma_l <- t(chol(sigma))
## measurement model
k <- 3
nu <- rep(x = 0, times = k)
lambda <- diag(k)
theta <- 0.2 * diag(k)
theta_l <- t(chol(theta))
boot <- PBSSMOUFixed(
R = 10L, # use at least 1000 in actual research
path = getwd(),
prefix = "ou",
n = n,
time = time,
delta_t = delta_t,
mu0 = mu0,
sigma0_l = sigma0_l,
mu = mu,
phi = phi,
sigma_l = sigma_l,
nu = nu,
lambda = lambda,
theta_l = theta_l,
ncores = NULL, # consider using multiple cores
seed = 42
)
phi_hat <- phi
colnames(phi_hat) <- rownames(phi_hat) <- c("x", "m", "y")
phi <- extract(object = boot, what = "phi")
# Specific time interval ----------------------------------------------------
BootBeta(
phi = phi,
phi_hat = phi_hat,
delta_t = 1
)
#>
#> Total, Direct, and Indirect Effects
#> type = pc
#> $`1`
#> interval est se R 2.5% 97.5%
#> from x to x 1 0.6998 0.0462 10 0.6266 0.7449
#> from x to m 1 0.5000 0.0248 10 0.4587 0.5299
#> from x to y 1 -0.1000 0.0135 10 -0.1302 -0.0931
#> from m to x 1 0.0000 0.0469 10 -0.0493 0.0834
#> from m to m 1 0.5999 0.0277 10 0.5667 0.6537
#> from m to y 1 0.3998 0.0171 10 0.3825 0.4322
#> from y to x 1 0.0000 0.0392 10 -0.0706 0.0489
#> from y to m 1 0.0000 0.0276 10 -0.0375 0.0443
#> from y to y 1 0.5001 0.0157 10 0.4886 0.5323
#>
# Range of time intervals ---------------------------------------------------
boot <- BootBeta(
phi = phi,
phi_hat = phi_hat,
delta_t = 1:5
)
plot(boot)
plot(boot, type = "bc") # bias-corrected
# Methods -------------------------------------------------------------------
# BootBeta has a number of methods including
# print, summary, confint, and plot
print(boot)
#>
#> Total, Direct, and Indirect Effects
#> type = pc
#> $`1`
#> interval est se R 2.5% 97.5%
#> from x to x 1 0.6998 0.0462 10 0.6266 0.7449
#> from x to m 1 0.5000 0.0248 10 0.4587 0.5299
#> from x to y 1 -0.1000 0.0135 10 -0.1302 -0.0931
#> from m to x 1 0.0000 0.0469 10 -0.0493 0.0834
#> from m to m 1 0.5999 0.0277 10 0.5667 0.6537
#> from m to y 1 0.3998 0.0171 10 0.3825 0.4322
#> from y to x 1 0.0000 0.0392 10 -0.0706 0.0489
#> from y to m 1 0.0000 0.0276 10 -0.0375 0.0443
#> from y to y 1 0.5001 0.0157 10 0.4886 0.5323
#>
#> $`2`
#> interval est se R 2.5% 97.5%
#> from x to x 2 0.4897 0.0483 10 0.4098 0.5591
#> from x to m 2 0.6499 0.0390 10 0.5798 0.6904
#> from x to y 2 0.0799 0.0159 10 0.0406 0.0879
#> from m to x 2 0.0000 0.0489 10 -0.0474 0.0818
#> from m to m 2 0.3599 0.0460 10 0.3184 0.4541
#> from m to y 2 0.4398 0.0195 10 0.4226 0.4788
#> from y to x 2 0.0000 0.0481 10 -0.0865 0.0616
#> from y to m 2 0.0000 0.0440 10 -0.0689 0.0554
#> from y to y 2 0.2501 0.0190 10 0.2345 0.2841
#>
#> $`3`
#> interval est se R 2.5% 97.5%
#> from x to x 3 0.3427 0.0463 10 0.2751 0.4257
#> from x to m 3 0.6347 0.0502 10 0.5459 0.7052
#> from x to y 3 0.2508 0.0187 10 0.2164 0.2668
#> from m to x 3 0.0000 0.0401 10 -0.0469 0.0612
#> from m to m 3 0.2159 0.0528 10 0.1761 0.3210
#> from m to y 3 0.3638 0.0247 10 0.3426 0.4109
#> from y to x 3 0.0000 0.0450 10 -0.0822 0.0574
#> from y to m 3 0.0000 0.0536 10 -0.0934 0.0546
#> from y to y 3 0.1251 0.0217 10 0.0991 0.1646
#>
#> $`4`
#> interval est se R 2.5% 97.5%
#> from x to x 4 0.2398 0.0451 10 0.1818 0.3288
#> from x to m 4 0.5521 0.0588 10 0.4572 0.6504
#> from x to y 4 0.3449 0.0247 10 0.2959 0.3704
#> from m to x 4 0.0000 0.0316 10 -0.0473 0.0417
#> from m to m 4 0.1295 0.0508 10 0.0907 0.2251
#> from m to y 4 0.2683 0.0311 10 0.2429 0.3363
#> from y to x 4 0.0000 0.0379 10 -0.0710 0.0473
#> from y to m 4 0.0000 0.0565 10 -0.1030 0.0564
#> from y to y 4 0.0625 0.0266 10 0.0262 0.1026
#>
#> $`5`
#> interval est se R 2.5% 97.5%
#> from x to x 5 0.1678 0.0436 10 0.1193 0.2574
#> from x to m 5 0.4511 0.0642 10 0.3589 0.5698
#> from x to y 5 0.3693 0.0323 10 0.3088 0.4065
#> from m to x 5 0.0000 0.0253 10 -0.0430 0.0354
#> from m to m 5 0.0777 0.0448 10 0.0312 0.1541
#> from m to y 5 0.1859 0.0344 10 0.1610 0.2617
#> from y to x 5 0.0000 0.0302 10 -0.0581 0.0366
#> from y to m 5 0.0000 0.0541 10 -0.1015 0.0562
#> from y to y 5 0.0313 0.0316 10 -0.0151 0.0702
#>
summary(boot)
#> effect interval est se R 2.5% 97.5%
#> 1 from x to x 1 0.69977250 0.04619116 10 0.62664729 0.74488459
#> 2 from x to m 1 0.50003412 0.02476283 10 0.45865329 0.52990640
#> 3 from x to y 1 -0.10003837 0.01352470 10 -0.13021799 -0.09314403
#> 4 from m to x 1 0.00000000 0.04693048 10 -0.04929444 0.08343532
#> 5 from m to m 1 0.59989538 0.02765975 10 0.56673563 0.65366698
#> 6 from m to y 1 0.39983562 0.01709394 10 0.38245910 0.43217031
#> 7 from y to x 1 0.00000000 0.03921752 10 -0.07064902 0.04890429
#> 8 from y to m 1 0.00000000 0.02757518 10 -0.03753362 0.04426060
#> 9 from y to y 1 0.50007360 0.01565101 10 0.48863283 0.53227520
#> 10 from x to x 2 0.48968155 0.04829661 10 0.40983641 0.55913746
#> 11 from x to m 2 0.64987829 0.03899876 10 0.57977635 0.69042092
#> 12 from x to y 2 0.07990080 0.01591422 10 0.04064558 0.08786268
#> 13 from m to x 2 0.00000000 0.04888590 10 -0.04743327 0.08178123
#> 14 from m to m 2 0.35987447 0.04599035 10 0.31838727 0.45406311
#> 15 from m to y 2 0.43980678 0.01949252 10 0.42255274 0.47879973
#> 16 from y to x 2 0.00000000 0.04808620 10 -0.08645868 0.06162203
#> 17 from y to m 2 0.00000000 0.04396104 10 -0.06887826 0.05544520
#> 18 from y to y 2 0.25007360 0.01902263 10 0.23452458 0.28407526
#> 19 from x to x 3 0.34266568 0.04625981 10 0.27505399 0.42572708
#> 20 from x to m 3 0.63471647 0.05020048 10 0.54592419 0.70521856
#> 21 from x to y 3 0.25081383 0.01873463 10 0.21635512 0.26676004
#> 22 from m to x 3 0.00000000 0.04013982 10 -0.04686850 0.06118365
#> 23 from m to m 3 0.21588703 0.05277385 10 0.17613806 0.32096736
#> 24 from m to y 3 0.36382639 0.02473911 10 0.34257063 0.41085799
#> 25 from y to x 3 0.00000000 0.04496705 10 -0.08215661 0.05740087
#> 26 from y to m 3 0.00000000 0.05360473 10 -0.09343319 0.05463893
#> 27 from y to y 3 0.12505520 0.02167083 10 0.09906528 0.16456126
#> 28 from x to x 4 0.23978802 0.04513964 10 0.18178975 0.32883844
#> 29 from x to m 4 0.55210801 0.05884353 10 0.45719753 0.65039899
#> 30 from x to y 4 0.34492791 0.02474916 10 0.29592103 0.37042957
#> 31 from m to x 4 0.00000000 0.03158889 10 -0.04732694 0.04168309
#> 32 from m to m 4 0.12950963 0.05084726 10 0.09070625 0.22505825
#> 33 from m to y 4 0.26825930 0.03113957 10 0.24288443 0.33626007
#> 34 from y to x 4 0.00000000 0.03785506 10 -0.07095595 0.04725816
#> 35 from y to m 4 0.00000000 0.05647188 10 -0.10303558 0.05638981
#> 36 from y to y 4 0.06253681 0.02659055 10 0.02623799 0.10262406
#> 37 from x to x 5 0.16779706 0.04357747 10 0.11929313 0.25743403
#> 38 from x to m 5 0.45110924 0.06420883 10 0.35894087 0.56976928
#> 39 from x to y 5 0.36925379 0.03226131 10 0.30878766 0.40647923
#> 40 from m to x 5 0.00000000 0.02531419 10 -0.04300933 0.03537615
#> 41 from m to m 5 0.07769223 0.04484573 10 0.03122991 0.15411817
#> 42 from m to y 5 0.18593196 0.03444554 10 0.16101445 0.26167942
#> 43 from y to x 5 0.00000000 0.03018798 10 -0.05814267 0.03661063
#> 44 from y to m 5 0.00000000 0.05406332 10 -0.10148472 0.05620318
#> 45 from y to y 5 0.03127301 0.03156738 10 -0.01509265 0.07019346
confint(boot, level = 0.95)
#> effect interval 2.5 % 97.5 %
#> 1 from x to x 1 0.62664729 0.74488459
#> 2 from x to m 1 0.45865329 0.52990640
#> 3 from x to y 1 -0.13021799 -0.09314403
#> 4 from x to x 2 0.40983641 0.55913746
#> 5 from x to m 2 0.57977635 0.69042092
#> 6 from x to y 2 0.04064558 0.08786268
#> 7 from x to x 3 0.27505399 0.42572708
#> 8 from x to m 3 0.54592419 0.70521856
#> 9 from x to y 3 0.21635512 0.26676004
#> 10 from x to x 4 0.18178975 0.32883844
#> 11 from x to m 4 0.45719753 0.65039899
#> 12 from x to y 4 0.29592103 0.37042957
#> 13 from x to x 5 0.11929313 0.25743403
#> 14 from x to m 5 0.35894087 0.56976928
#> 15 from x to y 5 0.30878766 0.40647923
print(boot, type = "bc") # bias-corrected
#>
#> Total, Direct, and Indirect Effects
#> type = bc
#> $`1`
#> interval est se R 2.5% 97.5%
#> from x to x 1 0.6998 0.0462 10 0.6247 0.7391
#> from x to m 1 0.5000 0.0248 10 0.4598 0.5310
#> from x to y 1 -0.1000 0.0135 10 -0.1193 -0.0928
#> from m to x 1 0.0000 0.0469 10 -0.0493 0.0834
#> from m to m 1 0.5999 0.0277 10 0.5653 0.6134
#> from m to y 1 0.3998 0.0171 10 0.3825 0.4322
#> from y to x 1 0.0000 0.0392 10 -0.0706 0.0489
#> from y to m 1 0.0000 0.0276 10 -0.0337 0.0487
#> from y to y 1 0.5001 0.0157 10 0.4886 0.5323
#>
#> $`2`
#> interval est se R 2.5% 97.5%
#> from x to x 2 0.4897 0.0483 10 0.3995 0.5203
#> from x to m 2 0.6499 0.0390 10 0.5718 0.6806
#> from x to y 2 0.0799 0.0159 10 0.0682 0.0888
#> from m to x 2 0.0000 0.0489 10 -0.0467 0.0820
#> from m to m 2 0.3599 0.0460 10 0.3177 0.4386
#> from m to y 2 0.4398 0.0195 10 0.4226 0.4634
#> from y to x 2 0.0000 0.0481 10 -0.0865 0.0616
#> from y to m 2 0.0000 0.0440 10 -0.0689 0.0554
#> from y to y 2 0.2501 0.0190 10 0.2339 0.2829
#>
#> $`3`
#> interval est se R 2.5% 97.5%
#> from x to x 3 0.3427 0.0463 10 0.2607 0.3854
#> from x to m 3 0.6347 0.0502 10 0.5323 0.6736
#> from x to y 3 0.2508 0.0187 10 0.2205 0.2683
#> from m to x 3 0.0000 0.0401 10 -0.0440 0.0617
#> from m to m 3 0.2159 0.0528 10 0.1761 0.3210
#> from m to y 3 0.3638 0.0247 10 0.3416 0.3980
#> from y to x 3 0.0000 0.0450 10 -0.0822 0.0574
#> from y to m 3 0.0000 0.0536 10 -0.0934 0.0546
#> from y to y 3 0.1251 0.0217 10 0.0990 0.1432
#>
#> $`4`
#> interval est se R 2.5% 97.5%
#> from x to x 4 0.2398 0.0451 10 0.1710 0.2551
#> from x to m 4 0.5521 0.0588 10 0.4374 0.5848
#> from x to y 4 0.3449 0.0247 10 0.3148 0.3716
#> from m to x 4 0.0000 0.0316 10 -0.0391 0.0422
#> from m to m 4 0.1295 0.0508 10 0.0907 0.2251
#> from m to y 4 0.2683 0.0311 10 0.2412 0.3233
#> from y to x 4 0.0000 0.0379 10 -0.0710 0.0473
#> from y to m 4 0.0000 0.0565 10 -0.1030 0.0564
#> from y to y 4 0.0625 0.0266 10 0.0246 0.0917
#>
#> $`5`
#> interval est se R 2.5% 97.5%
#> from x to x 5 0.1678 0.0436 10 0.1135 0.2148
#> from x to m 5 0.4511 0.0642 10 0.3371 0.5062
#> from x to y 5 0.3693 0.0323 10 0.2942 0.3981
#> from m to x 5 0.0000 0.0253 10 -0.0430 0.0354
#> from m to m 5 0.0777 0.0448 10 0.0412 0.1572
#> from m to y 5 0.1859 0.0344 10 0.1592 0.2470
#> from y to x 5 0.0000 0.0302 10 -0.0581 0.0366
#> from y to m 5 0.0000 0.0541 10 -0.1015 0.0562
#> from y to y 5 0.0313 0.0316 10 -0.0152 0.0641
#>
summary(boot, type = "bc")
#> effect interval est se R 2.5% 97.5%
#> 1 from x to x 1 0.69977250 0.04619116 10 0.62468140 0.73907938
#> 2 from x to m 1 0.50003412 0.02476283 10 0.45980840 0.53098923
#> 3 from x to y 1 -0.10003837 0.01352470 10 -0.11928264 -0.09276853
#> 4 from m to x 1 0.00000000 0.04693048 10 -0.04929444 0.08343532
#> 5 from m to m 1 0.59989538 0.02765975 10 0.56533542 0.61343471
#> 6 from m to y 1 0.39983562 0.01709394 10 0.38245910 0.43217031
#> 7 from y to x 1 0.00000000 0.03921752 10 -0.07064902 0.04890429
#> 8 from y to m 1 0.00000000 0.02757518 10 -0.03373034 0.04870959
#> 9 from y to y 1 0.50007360 0.01565101 10 0.48863283 0.53227520
#> 10 from x to x 2 0.48968155 0.04829661 10 0.39951058 0.52028969
#> 11 from x to m 2 0.64987829 0.03899876 10 0.57182354 0.68061666
#> 12 from x to y 2 0.07990080 0.01591422 10 0.06815270 0.08882083
#> 13 from m to x 2 0.00000000 0.04888590 10 -0.04673487 0.08197855
#> 14 from m to m 2 0.35987447 0.04599035 10 0.31766333 0.43855897
#> 15 from m to y 2 0.43980678 0.01949252 10 0.42255078 0.46342043
#> 16 from y to x 2 0.00000000 0.04808620 10 -0.08645868 0.06162203
#> 17 from y to m 2 0.00000000 0.04396104 10 -0.06887826 0.05544520
#> 18 from y to y 2 0.25007360 0.01902263 10 0.23392510 0.28285536
#> 19 from x to x 3 0.34266568 0.04625981 10 0.26069578 0.38535309
#> 20 from x to m 3 0.63471647 0.05020048 10 0.53225460 0.67358656
#> 21 from x to y 3 0.25081383 0.01873463 10 0.22048639 0.26829406
#> 22 from m to x 3 0.00000000 0.04013982 10 -0.04400360 0.06166691
#> 23 from m to m 3 0.21588703 0.05277385 10 0.17613806 0.32096736
#> 24 from m to y 3 0.36382639 0.02473911 10 0.34164309 0.39800899
#> 25 from y to x 3 0.00000000 0.04496705 10 -0.08215661 0.05740087
#> 26 from y to m 3 0.00000000 0.05360473 10 -0.09343319 0.05463893
#> 27 from y to y 3 0.12505520 0.02167083 10 0.09901812 0.14317853
#> 28 from x to x 4 0.23978802 0.04513964 10 0.17104675 0.25509649
#> 29 from x to m 4 0.55210801 0.05884353 10 0.43741315 0.58480548
#> 30 from x to y 4 0.34492791 0.02474916 10 0.31483437 0.37160448
#> 31 from m to x 4 0.00000000 0.03158889 10 -0.03909152 0.04223043
#> 32 from m to m 4 0.12950963 0.05084726 10 0.09070625 0.22505825
#> 33 from m to y 4 0.26825930 0.03113957 10 0.24118376 0.32331608
#> 34 from y to x 4 0.00000000 0.03785506 10 -0.07095595 0.04725816
#> 35 from y to m 4 0.00000000 0.05647188 10 -0.10303558 0.05638981
#> 36 from y to y 4 0.06253681 0.02659055 10 0.02457317 0.09166099
#> 37 from x to x 5 0.16779706 0.04357747 10 0.11350347 0.21483345
#> 38 from x to m 5 0.45110924 0.06420883 10 0.33710283 0.50621360
#> 39 from x to y 5 0.36925379 0.03226131 10 0.29418281 0.39806967
#> 40 from m to x 5 0.00000000 0.02531419 10 -0.04300933 0.03537615
#> 41 from m to m 5 0.07769223 0.04484573 10 0.04123415 0.15717773
#> 42 from m to y 5 0.18593196 0.03444554 10 0.15918697 0.24702743
#> 43 from y to x 5 0.00000000 0.03018798 10 -0.05814267 0.03661063
#> 44 from y to m 5 0.00000000 0.05406332 10 -0.10148472 0.05620318
#> 45 from y to y 5 0.03127301 0.03156738 10 -0.01516324 0.06407115
confint(boot, level = 0.95, type = "bc")
#> effect interval 2.5 % 97.5 %
#> 1 from x to x 1 0.6246814 0.73907938
#> 2 from x to m 1 0.4598084 0.53098923
#> 3 from x to y 1 -0.1192826 -0.09276853
#> 4 from x to x 2 0.3995106 0.52028969
#> 5 from x to m 2 0.5718235 0.68061666
#> 6 from x to y 2 0.0681527 0.08882083
#> 7 from x to x 3 0.2606958 0.38535309
#> 8 from x to m 3 0.5322546 0.67358656
#> 9 from x to y 3 0.2204864 0.26829406
#> 10 from x to x 4 0.1710467 0.25509649
#> 11 from x to m 4 0.4374131 0.58480548
#> 12 from x to y 4 0.3148344 0.37160448
#> 13 from x to x 5 0.1135035 0.21483345
#> 14 from x to m 5 0.3371028 0.50621360
#> 15 from x to y 5 0.2941828 0.39806967
# }