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Bootstrap Sampling Distribution for the Total Effect Centrality Over a Specific Time Interval or a Range of Time Intervals

Source: R/cTMed-boot-total-central.R
BootTotalCentral.Rd

This function generates a bootstrap method sampling distribution for the total effect centrality 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

BootTotalCentral(phi, phi_hat, delta_t, 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 (\(\Delta t\)).

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 ("BootTotalCentral").

output

A list with length of length(delta_t).

Each element in the output list has the following elements:

est

A vector of total effect centrality.

thetahatstar

A matrix of bootstrap total effect centrality.

Details

See TotalCentral() 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(), 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 ----------------------------------------------------
BootTotalCentral(
  phi = phi,
  phi_hat = phi_hat,
  delta_t = 1
)
#> 
#> Total Effect Centrality
#> type = pc
#> $`1`
#>   interval    est     se  R    2.5%  97.5%
#> x        1 0.4000 0.0230 10  0.3655 0.4264
#> m        1 0.3998 0.0477 10  0.3466 0.4918
#> y        1 0.0000 0.0589 10 -0.1013 0.0613
#> 

# Range of time intervals ---------------------------------------------------
boot <- BootTotalCentral(
  phi = phi,
  phi_hat = phi_hat,
  delta_t = 1:5
)
plot(boot)



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




# Methods -------------------------------------------------------------------
# BootTotalCentral has a number of methods including
# print, summary, confint, and plot
print(boot)
#> 
#> Total Effect Centrality
#> type = pc
#> $`1`
#>   interval    est     se  R    2.5%  97.5%
#> x        1 0.4000 0.0230 10  0.3655 0.4264
#> m        1 0.3998 0.0477 10  0.3466 0.4918
#> y        1 0.0000 0.0589 10 -0.1013 0.0613
#> 
#> $`2`
#>   interval    est     se  R    2.5%  97.5%
#> x        2 0.7298 0.0394 10  0.6503 0.7728
#> m        2 0.4398 0.0540 10  0.3823 0.5412
#> y        2 0.0000 0.0874 10 -0.1553 0.0890
#> 
#> $`3`
#>   interval    est     se  R    2.5%  97.5%
#> x        3 0.8855 0.0584 10  0.7695 0.9410
#> m        3 0.3638 0.0556 10  0.3091 0.4702
#> y        3 0.0000 0.0963 10 -0.1756 0.1031
#> 
#> $`4`
#>   interval    est     se  R    2.5%  97.5%
#> x        4 0.8970 0.0772 10  0.7551 0.9984
#> m        4 0.2683 0.0552 10  0.2212 0.3732
#> y        4 0.0000 0.0933 10 -0.1740 0.1013
#> 
#> $`5`
#>   interval    est     se  R    2.5%  97.5%
#> x        5 0.8204 0.0922 10  0.6677 0.9650
#> m        5 0.1859 0.0522 10  0.1407 0.2809
#> y        5 0.0000 0.0837 10 -0.1596 0.0905
#> 
summary(boot)
#>    variable interval       est         se  R       2.5%      97.5%
#> 1         x        1 0.3999957 0.02296759 10  0.3654829 0.42636204
#> 2         m        1 0.3998356 0.04772231 10  0.3465982 0.49180449
#> 3         y        1 0.0000000 0.05893594 10 -0.1013119 0.06128272
#> 4         x        2 0.7297791 0.03935772 10  0.6503308 0.77278373
#> 5         m        2 0.4398068 0.05403270 10  0.3823457 0.54118215
#> 6         y        2 0.0000000 0.08740366 10 -0.1553369 0.08899969
#> 7         x        3 0.8855303 0.05837274 10  0.7695357 0.94098257
#> 8         m        3 0.3638264 0.05562599 10  0.3091364 0.47021113
#> 9         y        3 0.0000000 0.09632624 10 -0.1755898 0.10308311
#> 10        x        4 0.8970359 0.07715246 10  0.7551021 0.99841198
#> 11        m        4 0.2682593 0.05517596 10  0.2211691 0.37320330
#> 12        y        4 0.0000000 0.09327282 10 -0.1739915 0.10128918
#> 13        x        5 0.8203630 0.09219479 10  0.6677285 0.96497207
#> 14        m        5 0.1859320 0.05222735 10  0.1407348 0.28089102
#> 15        y        5 0.0000000 0.08374104 10 -0.1596274 0.09052208
confint(boot, level = 0.95)
#>    variable interval      2.5 %     97.5 %
#> 1         x        1  0.3654829 0.42636204
#> 2         m        1  0.3465982 0.49180449
#> 3         y        1 -0.1013119 0.06128272
#> 4         x        2  0.6503308 0.77278373
#> 5         m        2  0.3823457 0.54118215
#> 6         y        2 -0.1553369 0.08899969
#> 7         x        3  0.7695357 0.94098257
#> 8         m        3  0.3091364 0.47021113
#> 9         y        3 -0.1755898 0.10308311
#> 10        x        4  0.7551021 0.99841198
#> 11        m        4  0.2211691 0.37320330
#> 12        y        4 -0.1739915 0.10128918
#> 13        x        5  0.6677285 0.96497207
#> 14        m        5  0.1407348 0.28089102
#> 15        y        5 -0.1596274 0.09052208
print(boot, type = "bc") # bias-corrected
#> 
#> Total Effect Centrality
#> type = bc
#> $`1`
#>   interval    est     se  R    2.5%  97.5%
#> x        1 0.4000 0.0230 10  0.3713 0.4282
#> m        1 0.3998 0.0477 10  0.3466 0.4918
#> y        1 0.0000 0.0589 10 -0.1013 0.0613
#> 
#> $`2`
#>   interval    est     se  R    2.5%  97.5%
#> x        2 0.7298 0.0394 10  0.6881 0.7794
#> m        2 0.4398 0.0540 10  0.3768 0.5391
#> y        2 0.0000 0.0874 10 -0.1553 0.0890
#> 
#> $`3`
#>   interval    est     se  R    2.5%  97.5%
#> x        3 0.8855 0.0584 10  0.7534 0.9384
#> m        3 0.3638 0.0556 10  0.3056 0.4642
#> y        3 0.0000 0.0963 10 -0.1756 0.1031
#> 
#> $`4`
#>   interval    est     se  R    2.5%  97.5%
#> x        4 0.8970 0.0772 10  0.7251 0.9572
#> m        4 0.2683 0.0552 10  0.2191 0.3633
#> y        4 0.0000 0.0933 10 -0.1740 0.1013
#> 
#> $`5`
#>   interval    est     se  R    2.5%  97.5%
#> x        5 0.8204 0.0922 10  0.6313 0.8943
#> m        5 0.1859 0.0522 10  0.1407 0.2809
#> y        5 0.0000 0.0837 10 -0.1596 0.0905
#> 
summary(boot, type = "bc")
#>    variable interval       est         se  R       2.5%      97.5%
#> 1         x        1 0.3999957 0.02296759 10  0.3712508 0.42824588
#> 2         m        1 0.3998356 0.04772231 10  0.3465982 0.49180449
#> 3         y        1 0.0000000 0.05893594 10 -0.1013119 0.06128272
#> 4         x        2 0.7297791 0.03935772 10  0.6881137 0.77938396
#> 5         m        2 0.4398068 0.05403270 10  0.3768249 0.53905183
#> 6         y        2 0.0000000 0.08740366 10 -0.1553369 0.08899969
#> 7         x        3 0.8855303 0.05837274 10  0.7534480 0.93837943
#> 8         m        3 0.3638264 0.05562599 10  0.3055505 0.46424140
#> 9         y        3 0.0000000 0.09632624 10 -0.1755898 0.10308311
#> 10        x        4 0.8970359 0.07715246 10  0.7250552 0.95717611
#> 11        m        4 0.2682593 0.05517596 10  0.2191289 0.36332567
#> 12        y        4 0.0000000 0.09327282 10 -0.1739915 0.10128918
#> 13        x        5 0.8203630 0.09219479 10  0.6312856 0.89432498
#> 14        m        5 0.1859320 0.05222735 10  0.1407348 0.28089102
#> 15        y        5 0.0000000 0.08374104 10 -0.1596274 0.09052208
confint(boot, level = 0.95, type = "bc")
#>    variable interval      2.5 %     97.5 %
#> 1         x        1  0.3712508 0.42824588
#> 2         m        1  0.3465982 0.49180449
#> 3         y        1 -0.1013119 0.06128272
#> 4         x        2  0.6881137 0.77938396
#> 5         m        2  0.3768249 0.53905183
#> 6         y        2 -0.1553369 0.08899969
#> 7         x        3  0.7534480 0.93837943
#> 8         m        3  0.3055505 0.46424140
#> 9         y        3 -0.1755898 0.10308311
#> 10        x        4  0.7250552 0.95717611
#> 11        m        4  0.2191289 0.36332567
#> 12        y        4 -0.1739915 0.10128918
#> 13        x        5  0.6312856 0.89432498
#> 14        m        5  0.1407348 0.28089102
#> 15        y        5 -0.1596274 0.09052208
# }