Total Effect Centrality

Total Effect Centrality

Usage

TotalCentral(phi, delta_t, tol = 0.01)

Arguments

phi

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

delta_t

Vector of positive numbers. Time interval (\(\Delta t\)).

tol

Numeric. Smallest possible time interval to allow.

Value

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

call

Function call.

args

Function arguments.

fun

Function used ("TotalCentral").

output

A matrix of total effect centrality.

Details

The total effect centrality of a variable is the sum of the total effects of a variable on all other variables at a particular time interval.

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(), 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(), 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")

# Specific time interval ----------------------------------------------------
TotalCentral(
  phi = phi,
  delta_t = 1
)
#> Call:
#> TotalCentral(phi = phi, delta_t = 1)
#> 
#> Total Effect Centrality
#> 
#>      interval   x      m y
#> [1,]        1 0.4 0.3998 0

# Range of time intervals ---------------------------------------------------
total_central <- TotalCentral(
  phi = phi,
  delta_t = 1:30
)
plot(total_central)


# Methods -------------------------------------------------------------------
# TotalCentral has a number of methods including
# print, summary, and plot
total_central <- TotalCentral(
  phi = phi,
  delta_t = 1:5
)
print(total_central)
#> Call:
#> TotalCentral(phi = phi, delta_t = 1:5)
#> 
#> Total Effect Centrality
#> 
#>      interval      x      m y
#> [1,]        1 0.4000 0.3998 0
#> [2,]        2 0.7298 0.4398 0
#> [3,]        3 0.8855 0.3638 0
#> [4,]        4 0.8970 0.2683 0
#> [5,]        5 0.8204 0.1859 0
summary(total_central)
#> Call:
#> TotalCentral(phi = phi, delta_t = 1:5)
#> 
#> Total Effect Centrality
#> 
#>      interval      x      m y
#> [1,]        1 0.4000 0.3998 0
#> [2,]        2 0.7298 0.4398 0
#> [3,]        3 0.8855 0.3638 0
#> [4,]        4 0.8970 0.2683 0
#> [5,]        5 0.8204 0.1859 0
plot(total_central)