cTMed (version 1.0.10)

PosteriorMedStd: Posterior Distribution of Standardized Total, Direct, and Indirect Effects of X on Y Through M Over a Specific Time Interval or a Range of Time Intervals

Description

This function generates a posterior distribution of the standardized 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 posterior distribution of the first-order stochastic differential equation model drift matrix \(\boldsymbol{\Phi}\) and process noise covariance matrix \(\boldsymbol{\Sigma}\).

Usage

PosteriorMedStd(phi, sigma, delta_t, from, to, med, ncores = NULL, tol = 0.001)

Value

Returns an object of class ctmedmc which is a list with the following elements:

call

Function call.

args

Function arguments.

fun

Function used ("PosteriorMedStd").

output

A list of length length(delta_t).

Each element in the output list has the following elements:

est

Mean of the posterior distribution of the standardized total, direct, and indirect effects.

thetahatstar

Posterior distribution of the standardized total, direct, and indirect effects.

Arguments

phi

List of numeric matrices. Each element of the list is a sample from the posterior distribution of the drift matrix (\(\boldsymbol{\Phi}\)). Each matrix should have row and column names pertaining to the variables in the system.

sigma

List of numeric matrices. Each element of the list is a sample from the posterior distribution of the process noise covariance matrix (\(\boldsymbol{\Sigma}\)). Each matrix 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.

Author

Ivan Jacob Agaloos Pesigan

Details

See TotalStd(), DirectStd(), and IndirectStd() for more details.

References

Bollen, K. A. (1987). Total, direct, and indirect effects in structural equation models. Sociological Methodology, 17, 37. tools:::Rd_expr_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. tools:::Rd_expr_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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1007/s11336-021-09767-0")

See Also

Other Continuous-Time Mediation Functions: BootBeta(), BootBetaStd(), BootDirectCentral(), BootDirectCentralStd(), BootIndirectCentral(), BootIndirectCentralStd(), BootMed(), BootMedStd(), BootTotalCentral(), BootTotalCentralStd(), 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(), PosteriorTotalCentral(), PosteriorTotalCentralStd(), Total(), TotalCentral(), TotalCentralStd(), TotalStd(), Trajectory()

Examples

set.seed(42)
phi <- matrix(
  data = c(
    -0.357, 0.771, -0.450,
    0.000, -0.511, 0.729,
    0.000, 0.000, -0.693
  ),
  nrow = 3
)
colnames(phi) <- rownames(phi) <- c("x", "m", "y")
sigma <- matrix(
  data = c(
    0.24455556, 0.02201587, -0.05004762,
    0.02201587, 0.07067800, 0.01539456,
    -0.05004762, 0.01539456, 0.07553061
  ),
  nrow = 3
)
colnames(sigma) <- rownames(sigma) <- c("x", "m", "y")
input <- MCPhiSigma(
  phi = phi,
  sigma = sigma,
  vcov_theta = 0.001 * diag(15),
  R = 100L,
  seed = 42
)$output
phi <- lapply(
  X = input,
  FUN = function(x) {
    x[[1]]
  }
)
sigma <- lapply(
  X = input,
  FUN = function(x) {
    x[[2]]
  }
)

# Specific time interval ----------------------------------------------------
PosteriorMedStd(
  phi = phi,
  sigma = sigma,
  delta_t = 1,
  from = "x",
  to = "y",
  med = "m"
)

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

# Methods -------------------------------------------------------------------
# PosteriorMedStd has a number of methods including
# print, summary, confint, and plot
print(posterior)
summary(posterior)
confint(posterior, level = 0.95)
plot(posterior)