PosteriorMed: Posterior Distribution of 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 total, direct and indirect effects of the independent variable $X$ on the dependent variable $Y$ through mediator variables $m$ over a specific time interval $Δ t$ or a range of time intervals using the posterior distribution of the first-order stochastic differential equation model drift matrix $Φ$ .

Usage

PosteriorMed(phi, delta_t, from, to, med, ncores = NULL, tol = 0.01)

Value

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

call: Function call.
args: Function arguments.
fun: Function used ("PosteriorMed").
output: A list the length of which is equal to the length of delta_t.

Each element in the output list has the following elements:

est: Mean of the posterior distribution of the total, direct, and indirect effects.
thetahatstar: Posterior distribution of the 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 ( $Φ$ ). Each matrix should have row and column names pertaining to the variables in the system.
delta_t: Numeric. Time interval ( $Δ t$ ).
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 Total(), Direct(), and Indirect() 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")

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")

Examples

Run this code

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")
vcov_phi_vec <- matrix(
  data = c(
    0.00843, 0.00040, -0.00151,
    -0.00600, -0.00033, 0.00110,
    0.00324, 0.00020, -0.00061,
    0.00040, 0.00374, 0.00016,
    -0.00022, -0.00273, -0.00016,
    0.00009, 0.00150, 0.00012,
    -0.00151, 0.00016, 0.00389,
    0.00103, -0.00007, -0.00283,
    -0.00050, 0.00000, 0.00156,
    -0.00600, -0.00022, 0.00103,
    0.00644, 0.00031, -0.00119,
    -0.00374, -0.00021, 0.00070,
    -0.00033, -0.00273, -0.00007,
    0.00031, 0.00287, 0.00013,
    -0.00014, -0.00170, -0.00012,
    0.00110, -0.00016, -0.00283,
    -0.00119, 0.00013, 0.00297,
    0.00063, -0.00004, -0.00177,
    0.00324, 0.00009, -0.00050,
    -0.00374, -0.00014, 0.00063,
    0.00495, 0.00024, -0.00093,
    0.00020, 0.00150, 0.00000,
    -0.00021, -0.00170, -0.00004,
    0.00024, 0.00214, 0.00012,
    -0.00061, 0.00012, 0.00156,
    0.00070, -0.00012, -0.00177,
    -0.00093, 0.00012, 0.00223
  ),
  nrow = 9
)

phi <- MCPhi(
  phi = phi,
  vcov_phi_vec = vcov_phi_vec,
  R = 1000L
)$output

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

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

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

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