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

This function generates a bootstrap method sampling distribution for the standardized 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 \(\boldsymbol{\Phi}\) and process noise covariance matrix \(\boldsymbol{\Sigma}\).

Usage

BootTotalCentralStd(
  phi,
  sigma,
  phi_hat,
  sigma_hat,
  delta_t,
  ncores = NULL,
  tol = 0.001
)

Arguments

phi

List of numeric matrices. Each element of the list is a bootstrap estimate of the drift matrix (\(\boldsymbol{\Phi}\)).

sigma

List of numeric matrices. Each element of the list is a bootstrap estimate of the process noise covariance matrix (\(\boldsymbol{\Sigma}\)).

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.

sigma_hat

Numeric matrix. The estimated process noise covariance matrix (\(\hat{\boldsymbol{\Sigma}}\)) from the original data set.

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 ("BootTotalCentralStd").

output

A list of length length(delta_t).

Each element in the output list has the following elements:

est

A vector of standardized total effect centrality.

thetahatstar

A matrix of bootstrap standardized total effect centrality.

Details

See TotalCentralStd() 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

Pesigan, I. J. A., Russell, M. A., & Chow, S.-M. (2025). Inferences and effect sizes for direct, indirect, and total effects in continuous-time mediation models. Psychological Methods. doi:10.1037/met0000779

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(), BootDirectCentral(), BootDirectCentralStd(), BootIndirectCentral(), BootIndirectCentralStd(), BootMed(), BootMedStd(), BootTotalCentral(), DeltaBeta(), DeltaBetaStd(), DeltaDirectCentral(), DeltaDirectCentralStd(), DeltaIndirectCentral(), DeltaMed(), DeltaMedStd(), DeltaTotalCentral(), DeltaTotalCentralStd(), Direct(), DirectCentral(), DirectCentralStd(), DirectStd(), Indirect(), IndirectCentral(), IndirectCentralStd(), IndirectStd(), MCBeta(), MCBetaStd(), MCDirectCentral(), MCDirectCentralStd(), MCIndirectCentral(), MCIndirectCentralStd(), MCMed(), MCMedStd(), MCPhi(), MCPhiSigma(), MCTotalCentral(), MCTotalCentralStd(), Med(), MedStd(), PosteriorBeta(), PosteriorBetaStd(), PosteriorDirectCentral(), PosteriorDirectCentralStd(), PosteriorIndirectCentral(), PosteriorIndirectCentralStd(), PosteriorMed(), PosteriorMedStd(), PosteriorTotalCentral(), PosteriorTotalCentralStd(), Total(), TotalCentral(), TotalCentralStd(), TotalStd(), Trajectory()

Author

Ivan Jacob Agaloos Pesigan

Examples

if (FALSE) { # \dontrun{
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
sigma_hat <- sigma
colnames(phi_hat) <- rownames(phi_hat) <- c("x", "m", "y")
phi <- extract(object = boot, what = "phi")
sigma <- extract(object = boot, what = "sigma")

# Specific time interval ----------------------------------------------------
BootTotalCentralStd(
  phi = phi,
  sigma = sigma,
  phi_hat = phi_hat,
  sigma_hat = sigma_hat,
  delta_t = 1
)

# Range of time intervals ---------------------------------------------------
boot <- BootTotalCentralStd(
  phi = phi,
  sigma = sigma,
  phi_hat = phi_hat,
  sigma_hat = sigma_hat,
  delta_t = 1:5
)
plot(boot)
plot(boot, type = "bc") # bias-corrected

# Methods -------------------------------------------------------------------
# BootTotalCentralStd has a number of methods including
# print, summary, confint, and plot
print(boot)
summary(boot)
confint(boot, level = 0.95)
print(boot, type = "bc") # bias-corrected
summary(boot, type = "bc")
confint(boot, level = 0.95, type = "bc")
} # }