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Bootstrap Sampling 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-boot-med.R
BootMed.Rd

This function generates a bootstrap method sampling 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 first-order stochastic differential equation model drift matrix \(\boldsymbol{\Phi}\).

Usage

BootMed(phi, phi_hat, delta_t, from, to, med, ncores = NULL, tol = 0.01)

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_hat 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 replications R is 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 ("BootMed").

output

A list with length of length(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 bootstrap 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(), 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()

Author

Ivan Jacob Agaloos Pesigan

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 ----------------------------------------------------
BootMed(
  phi = phi,
  phi_hat = phi_hat,
  delta_t = 1,
  from = "x",
  to = "y",
  med = "m"
)
#> 
#> Total, Direct, and Indirect Effects
#> type = pc
#> $`1`
#>          interval     est     se  R    2.5%   97.5%
#> total           1 -0.1000 0.0135 10 -0.1302 -0.0931
#> direct          1 -0.2675 0.0235 10 -0.3051 -0.2387
#> indirect        1  0.1674 0.0140 10  0.1449  0.1826
#> 

# Range of time intervals ---------------------------------------------------
boot <- BootMed(
  phi = phi,
  phi_hat = phi_hat,
  delta_t = 1:5,
  from = "x",
  to = "y",
  med = "m"
)
plot(boot)



plot(boot, type = "bc") # bias-corrected




# Methods -------------------------------------------------------------------
# BootMed 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%
#> total           1 -0.1000 0.0135 10 -0.1302 -0.0931
#> direct          1 -0.2675 0.0235 10 -0.3051 -0.2387
#> indirect        1  0.1674 0.0140 10  0.1449  0.1826
#> 
#> $`2`
#>          interval     est     se  R    2.5%   97.5%
#> total           2  0.0799 0.0159 10  0.0406  0.0879
#> direct          2 -0.3209 0.0367 10 -0.3745 -0.2717
#> indirect        2  0.4008 0.0354 10  0.3411  0.4391
#> 
#> $`3`
#>          interval     est     se  R    2.5%   97.5%
#> total           3  0.2508 0.0187 10  0.2164  0.2668
#> direct          3 -0.2914 0.0441 10 -0.3521 -0.2338
#> indirect        3  0.5423 0.0539 10  0.4524  0.6029
#> 
#> $`4`
#>          interval     est     se  R    2.5%   97.5%
#> total           4  0.3449 0.0247 10  0.2959  0.3704
#> direct          4 -0.2374 0.0455 10 -0.2993 -0.1775
#> indirect        4  0.5823 0.0657 10  0.4754  0.6638
#> 
#> $`5`
#>          interval     est     se  R    2.5%   97.5%
#> total           5  0.3693 0.0323 10  0.3088  0.4065
#> direct          5 -0.1828 0.0426 10 -0.2425 -0.1273
#> indirect        5  0.5521 0.0710 10  0.4361  0.6438
#> 
summary(boot)
#>      effect interval        est         se  R        2.5%       97.5%
#> 1     total        1 -0.1000384 0.01352470 10 -0.13021799 -0.09314403
#> 2    direct        1 -0.2674539 0.02346151 10 -0.30506209 -0.23871488
#> 3  indirect        1  0.1674155 0.01401604 10  0.14494208  0.18255013
#> 4     total        2  0.0799008 0.01591422 10  0.04064558  0.08786268
#> 5    direct        2 -0.3209035 0.03672873 10 -0.37450426 -0.27173260
#> 6  indirect        2  0.4008043 0.03541841 10  0.34113848  0.43908776
#> 7     total        3  0.2508138 0.01873463 10  0.21635512  0.26676004
#> 8    direct        3 -0.2914426 0.04411314 10 -0.35208890 -0.23382113
#> 9  indirect        3  0.5422564 0.05386335 10  0.45235059  0.60293039
#> 10    total        4  0.3449279 0.02474916 10  0.29592103  0.37042957
#> 11   direct        4 -0.2373900 0.04547156 10 -0.29927095 -0.17754396
#> 12 indirect        4  0.5823179 0.06568261 10  0.47544857  0.66375150
#> 13    total        5  0.3692538 0.03226131 10  0.30878766  0.40647923
#> 14   direct        5 -0.1828447 0.04263584 10 -0.24246640 -0.12727444
#> 15 indirect        5  0.5520985 0.07097678 10  0.43606210  0.64375063
confint(boot, level = 0.95)
#>      effect interval       2.5 %      97.5 %
#> 1     total        1 -0.13021799 -0.09314403
#> 2    direct        1 -0.30506209 -0.23871488
#> 3  indirect        1  0.14494208  0.18255013
#> 4     total        2  0.04064558  0.08786268
#> 5    direct        2 -0.37450426 -0.27173260
#> 6  indirect        2  0.34113848  0.43908776
#> 7     total        3  0.21635512  0.26676004
#> 8    direct        3 -0.35208890 -0.23382113
#> 9  indirect        3  0.45235059  0.60293039
#> 10    total        4  0.29592103  0.37042957
#> 11   direct        4 -0.29927095 -0.17754396
#> 12 indirect        4  0.47544857  0.66375150
#> 13    total        5  0.30878766  0.40647923
#> 14   direct        5 -0.24246640 -0.12727444
#> 15 indirect        5  0.43606210  0.64375063
print(boot, type = "bc") # bias-corrected
#> 
#> Total, Direct, and Indirect Effects
#> type = bc
#> $`1`
#>          interval     est     se  R    2.5%   97.5%
#> total           1 -0.1000 0.0135 10 -0.1193 -0.0928
#> direct          1 -0.2675 0.0235 10 -0.2886 -0.2386
#> indirect        1  0.1674 0.0140 10  0.1449  0.1826
#> 
#> $`2`
#>          interval     est     se  R    2.5%   97.5%
#> total           2  0.0799 0.0159 10  0.0682  0.0888
#> direct          2 -0.3209 0.0367 10 -0.3662 -0.2699
#> indirect        2  0.4008 0.0354 10  0.3440  0.4398
#> 
#> $`3`
#>          interval     est     se  R    2.5%   97.5%
#> total           3  0.2508 0.0187 10  0.2205  0.2683
#> direct          3 -0.2914 0.0441 10 -0.3368 -0.2290
#> indirect        3  0.5423 0.0539 10  0.4451  0.5950
#> 
#> $`4`
#>          interval     est     se  R    2.5%   97.5%
#> total           4  0.3449 0.0247 10  0.3148  0.3716
#> direct          4 -0.2374 0.0455 10 -0.2836 -0.1738
#> indirect        4  0.5823 0.0657 10  0.4605  0.6425
#> 
#> $`5`
#>          interval     est     se  R    2.5%   97.5%
#> total           5  0.3693 0.0323 10  0.2942  0.3981
#> direct          5 -0.1828 0.0426 10 -0.2298 -0.1242
#> indirect        5  0.5521 0.0710 10  0.4184  0.6273
#> 
summary(boot, type = "bc")
#>      effect interval        est         se  R       2.5%       97.5%
#> 1     total        1 -0.1000384 0.01352470 10 -0.1192826 -0.09276853
#> 2    direct        1 -0.2674539 0.02346151 10 -0.2885540 -0.23858310
#> 3  indirect        1  0.1674155 0.01401604 10  0.1449421  0.18255013
#> 4     total        2  0.0799008 0.01591422 10  0.0681527  0.08882083
#> 5    direct        2 -0.3209035 0.03672873 10 -0.3661783 -0.26985895
#> 6  indirect        2  0.4008043 0.03541841 10  0.3439750  0.43979905
#> 7     total        3  0.2508138 0.01873463 10  0.2204864  0.26829406
#> 8    direct        3 -0.2914426 0.04411314 10 -0.3368455 -0.22903334
#> 9  indirect        3  0.5422564 0.05386335 10  0.4450868  0.59498768
#> 10    total        4  0.3449279 0.02474916 10  0.3148344  0.37160448
#> 11   direct        4 -0.2373900 0.04547156 10 -0.2835681 -0.17381101
#> 12 indirect        4  0.5823179 0.06568261 10  0.4605166  0.64249685
#> 13    total        5  0.3692538 0.03226131 10  0.2941828  0.39806967
#> 14   direct        5 -0.1828447 0.04263584 10 -0.2297977 -0.12421649
#> 15 indirect        5  0.5520985 0.07097678 10  0.4183993  0.62725485
confint(boot, level = 0.95, type = "bc")
#>      effect interval      2.5 %      97.5 %
#> 1     total        1 -0.1192826 -0.09276853
#> 2    direct        1 -0.2885540 -0.23858310
#> 3  indirect        1  0.1449421  0.18255013
#> 4     total        2  0.0681527  0.08882083
#> 5    direct        2 -0.3661783 -0.26985895
#> 6  indirect        2  0.3439750  0.43979905
#> 7     total        3  0.2204864  0.26829406
#> 8    direct        3 -0.3368455 -0.22903334
#> 9  indirect        3  0.4450868  0.59498768
#> 10    total        4  0.3148344  0.37160448
#> 11   direct        4 -0.2835681 -0.17381101
#> 12 indirect        4  0.4605166  0.64249685
#> 13    total        5  0.2941828  0.39806967
#> 14   direct        5 -0.2297977 -0.12421649
#> 15 indirect        5  0.4183993  0.62725485
# }