BootBeta {cTMed} | R Documentation |
Bootstrap Sampling Distribution for the Elements of the Matrix of Lagged Coefficients Over a Specific Time Interval or a Range of Time Intervals
Description
This 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}
.
Usage
BootBeta(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 ( |
phi_hat |
Numeric matrix.
The estimated drift matrix ( |
delta_t |
Numeric.
Time interval
( |
ncores |
Positive integer.
Number of cores to use.
If |
tol |
Numeric. Smallest possible time interval to allow. |
Details
See Total()
.
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.
Author(s)
Ivan Jacob Agaloos Pesigan
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
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
)
# 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)
summary(boot)
confint(boot, level = 0.95)
print(boot, type = "bc") # bias-corrected
summary(boot, type = "bc")
confint(boot, level = 0.95, type = "bc")