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)
#> NULL
plot(boot, type = "bc") # bias-corrected
#> NULL
# 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 0.04619127 10 0.62664729 0.74488486
#> 2 from x to m 1 0.50003412 0.02476280 10 0.45865329 0.52990642
#> 3 from x to y 1 -0.10003837 0.01352464 10 -0.13021792 -0.09314403
#> 4 from m to x 1 0.00000000 0.04693076 10 -0.04929605 0.08343531
#> 5 from m to m 1 0.59989538 0.02765981 10 0.56673562 0.65366698
#> 6 from m to y 1 0.39983562 0.01709393 10 0.38245910 0.43217027
#> 7 from y to x 1 0.00000000 0.03921769 10 -0.07064900 0.04890509
#> 8 from y to m 1 0.00000000 0.02757517 10 -0.03753362 0.04426060
#> 9 from y to y 1 0.50007360 0.01565101 10 0.48863283 0.53227519
#> 10 from x to x 2 0.48968155 0.04829663 10 0.40983641 0.55913746
#> 11 from x to m 2 0.64987829 0.03899877 10 0.57977635 0.69042094
#> 12 from x to y 2 0.07990080 0.01591419 10 0.04064558 0.08786268
#> 13 from m to x 2 0.00000000 0.04888617 10 -0.04743381 0.08178123
#> 14 from m to m 2 0.35987447 0.04599063 10 0.31838726 0.45406311
#> 15 from m to y 2 0.43980678 0.01949248 10 0.42255275 0.47879968
#> 16 from y to x 2 0.00000000 0.04808642 10 -0.08645866 0.06162306
#> 17 from y to m 2 0.00000000 0.04396116 10 -0.06887824 0.05544520
#> 18 from y to y 2 0.25007360 0.01902263 10 0.23452458 0.28407525
#> 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 0.01873460 10 0.21635512 0.26676004
#> 22 from m to x 3 0.00000000 0.04013996 10 -0.04686844 0.06118365
#> 23 from m to m 3 0.21588703 0.05277420 10 0.17613732 0.32096736
#> 24 from m to y 3 0.36382639 0.02473914 10 0.34257062 0.41085797
#> 25 from y to x 3 0.00000000 0.04496726 10 -0.08215659 0.05740182
#> 26 from y to m 3 0.00000000 0.05360494 10 -0.09343317 0.05463939
#> 27 from y to y 3 0.12505520 0.02167084 10 0.09906528 0.16456126
#> 28 from x to x 4 0.23978802 0.04513966 10 0.18178975 0.32883844
#> 29 from x to m 4 0.55210801 0.05884355 10 0.45719753 0.65039899
#> 30 from x to y 4 0.34492791 0.02474912 10 0.29592102 0.37042958
#> 31 from m to x 4 0.00000000 0.03158891 10 -0.04732685 0.04168309
#> 32 from m to m 4 0.12950963 0.05084755 10 0.09070564 0.22505825
#> 33 from m to y 4 0.26825930 0.03113970 10 0.24288441 0.33626007
#> 34 from y to x 4 0.00000000 0.03785522 10 -0.07095592 0.04725892
#> 35 from y to m 4 0.00000000 0.05647212 10 -0.10303555 0.05639129
#> 36 from y to y 4 0.06253681 0.02659062 10 0.02623799 0.10262406
#> 37 from x to x 5 0.16779706 0.04357748 10 0.11929314 0.25743403
#> 38 from x to m 5 0.45110924 0.06420888 10 0.35894087 0.56976928
#> 39 from x to y 5 0.36925379 0.03226128 10 0.30878766 0.40647923
#> 40 from m to x 5 0.00000000 0.02531414 10 -0.04300923 0.03537615
#> 41 from m to m 5 0.07769223 0.04484591 10 0.03122999 0.15411818
#> 42 from m to y 5 0.18593196 0.03444572 10 0.16101443 0.26167942
#> 43 from y to x 5 0.00000000 0.03018809 10 -0.05814265 0.03661118
#> 44 from y to m 5 0.00000000 0.05406353 10 -0.10148469 0.05620444
#> 45 from y to y 5 0.03127301 0.03156750 10 -0.01509265 0.07019373
confint(boot, level = 0.95)
#> effect interval 2.5 % 97.5 %
#> 1 from x to x 1 0.62664729 0.74488486
#> 2 from x to m 1 0.45865329 0.52990642
#> 3 from x to y 1 -0.13021792 -0.09314403
#> 4 from x to x 2 0.40983641 0.55913746
#> 5 from x to m 2 0.57977635 0.69042094
#> 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 0.29592102 0.37042958
#> 13 from x to x 5 0.11929314 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 0.04619127 10 0.62468140 0.73907982
#> 2 from x to m 1 0.50003412 0.02476280 10 0.45980839 0.53098926
#> 3 from x to y 1 -0.10003837 0.01352464 10 -0.11928264 -0.09276852
#> 4 from m to x 1 0.00000000 0.04693076 10 -0.04929605 0.08343531
#> 5 from m to m 1 0.59989538 0.02765981 10 0.56533542 0.61343471
#> 6 from m to y 1 0.39983562 0.01709393 10 0.38245910 0.43217027
#> 7 from y to x 1 0.00000000 0.03921769 10 -0.07064900 0.04890509
#> 8 from y to m 1 0.00000000 0.02757517 10 -0.03373034 0.04870959
#> 9 from y to y 1 0.50007360 0.01565101 10 0.48863283 0.53227519
#> 10 from x to x 2 0.48968155 0.04829663 10 0.39951058 0.52029002
#> 11 from x to m 2 0.64987829 0.03899877 10 0.57182354 0.68061666
#> 12 from x to y 2 0.07990080 0.01591419 10 0.06815270 0.08882083
#> 13 from m to x 2 0.00000000 0.04888617 10 -0.04673642 0.08197855
#> 14 from m to m 2 0.35987447 0.04599063 10 0.31766332 0.43855897
#> 15 from m to y 2 0.43980678 0.01949248 10 0.42255079 0.46342043
#> 16 from y to x 2 0.00000000 0.04808642 10 -0.08645866 0.06162306
#> 17 from y to m 2 0.00000000 0.04396116 10 -0.06887824 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 0.38535308
#> 20 from x to m 3 0.63471647 0.05020048 10 0.53225460 0.67358657
#> 21 from x to y 3 0.25081383 0.01873460 10 0.22048639 0.26829407
#> 22 from m to x 3 0.00000000 0.04013996 10 -0.04400358 0.06166691
#> 23 from m to m 3 0.21588703 0.05277420 10 0.17613732 0.32096736
#> 24 from m to y 3 0.36382639 0.02473914 10 0.34164307 0.39800896
#> 25 from y to x 3 0.00000000 0.04496726 10 -0.08215659 0.05740182
#> 26 from y to m 3 0.00000000 0.05360494 10 -0.09343317 0.05463939
#> 27 from y to y 3 0.12505520 0.02167084 10 0.09901812 0.14317853
#> 28 from x to x 4 0.23978802 0.04513966 10 0.17104675 0.25509649
#> 29 from x to m 4 0.55210801 0.05884355 10 0.43741315 0.58480548
#> 30 from x to y 4 0.34492791 0.02474912 10 0.31483437 0.37160448
#> 31 from m to x 4 0.00000000 0.03158891 10 -0.03909148 0.04223043
#> 32 from m to m 4 0.12950963 0.05084755 10 0.09070564 0.22505825
#> 33 from m to y 4 0.26825930 0.03113970 10 0.24118373 0.32331608
#> 34 from y to x 4 0.00000000 0.03785522 10 -0.07095592 0.04725892
#> 35 from y to m 4 0.00000000 0.05647212 10 -0.10303555 0.05639129
#> 36 from y to y 4 0.06253681 0.02659062 10 0.02457317 0.09166099
#> 37 from x to x 5 0.16779706 0.04357748 10 0.11350347 0.21483344
#> 38 from x to m 5 0.45110924 0.06420888 10 0.33710283 0.50621358
#> 39 from x to y 5 0.36925379 0.03226128 10 0.29418281 0.39806966
#> 40 from m to x 5 0.00000000 0.02531414 10 -0.04300923 0.03537615
#> 41 from m to m 5 0.07769223 0.04484591 10 0.04123419 0.15717775
#> 42 from m to y 5 0.18593196 0.03444572 10 0.15918694 0.24702743
#> 43 from y to x 5 0.00000000 0.03018809 10 -0.05814265 0.03661118
#> 44 from y to m 5 0.00000000 0.05406353 10 -0.10148469 0.05620444
#> 45 from y to y 5 0.03127301 0.03156750 10 -0.01516323 0.06407193
confint(boot, level = 0.95, type = "bc")
#> effect interval 2.5 % 97.5 %
#> 1 from x to x 1 0.6246814 0.73907982
#> 2 from x to m 1 0.4598084 0.53098926
#> 3 from x to y 1 -0.1192826 -0.09276852
#> 4 from x to x 2 0.3995106 0.52029002
#> 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 0.38535308
#> 8 from x to m 3 0.5322546 0.67358657
#> 9 from x to y 3 0.2204864 0.26829407
#> 10 from x to x 4 0.1710467 0.25509649
#> 11 from x to m 4 0.4374132 0.58480548
#> 12 from x to y 4 0.3148344 0.37160448
#> 13 from x to x 5 0.1135035 0.21483344
#> 14 from x to m 5 0.3371028 0.50621358
#> 15 from x to y 5 0.2941828 0.39806966
# }