Standardized Indirect Effect of X on Y Through M Over a Specific Time Interval

This function computes the standardized indirect effect of the independent variable \(X\) on the dependent variable \(Y\) through mediator variables \(\mathbf{m}\) over a specific time interval \(\Delta t\) using the first-order stochastic differential equation model's drift matrix \(\boldsymbol{\Phi}\) and process noise covariance matrix \(\boldsymbol{\Sigma}\).

Usage

IndirectStd(phi, sigma, delta_t, from, to, med)

Arguments

phi

Numeric matrix. The drift matrix (\(\boldsymbol{\Phi}\)). phi should have row and column names pertaining to the variables in the system.

sigma

Numeric matrix. The process noise covariance matrix (\(\boldsymbol{\Sigma}\)).

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.

Value

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

call

Function call.

args

Function arguments.

fun

Function used ("IndirectStd").

output

The indirect effect.

Details

The standardized indirect effect of the independent variable \(X\) on the dependent variable \(Y\) relative to some mediator variables \(\mathbf{m}\) over a specific time interval \(\Delta t\) is given by $$ \mathrm{Indirect}^{\ast}_{{\Delta t}_{i, j}} = \mathrm{Total}^{\ast}_{\Delta t} - \mathrm{Direct}^{\ast}_{\Delta t} $$ where \(\mathrm{Total}^{\ast}_{\Delta t}\) and \(\mathrm{Direct}^{\ast}_{\Delta t}\) are standardized total and direct effects for time interval \(\Delta t\).

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: DeltaBeta(), DeltaBetaStd(), DeltaIndirectCentral(), DeltaMed(), DeltaMedStd(), DeltaTotalCentral(), Direct(), DirectStd(), ExpCov(), ExpMean(), Indirect(), IndirectCentral(), MCBeta(), MCBetaStd(), MCIndirectCentral(), MCMed(), MCMedStd(), MCPhi(), MCTotalCentral(), Med(), MedStd(), PosteriorBeta(), PosteriorIndirectCentral(), PosteriorMed(), PosteriorPhi(), PosteriorTotalCentral(), Total(), TotalCentral(), TotalStd(), Trajectory()

Author

Ivan Jacob Agaloos Pesigan

Examples

phi <- matrix(
  data = c(
    -0.357, 0.771, -0.450,
    0.0, -0.511, 0.729,
    0, 0, -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
)
delta_t <- 1
IndirectStd(
  phi = phi,
  sigma = sigma,
  delta_t = delta_t,
  from = "x",
  to = "y",
  med = "m"
)
#> [1] 0.1567