total_effect: Calculate total effects

In dsem: Dynamic Structural Equation Models

Calculate total effects

Description

Calculate a data frame of total effects, resulting from a pulse experiment (i.e., an exogenous and temporary change in a single variable in time t=0) or a press experiment (i.e., an exogenous and permanent change in a single variable starting in time t=0 and continuing for n_lags times), representing the estimated effect of a change in any variable on every other variable and any time-lag from 0 (simultaneous effects) to a user-specified maximum lag.

Usage

total_effect(object, n_lags = 4, type = c("pulse", "press"))

Arguments

object	Output from dsem
n_lags	Number of lags over which to calculate total effects
type	Whether a pulse or press experiment is intended. A pulse experiment answers the question: ⁠What happens if a variable is changed for only a single time-interval?" A press experiment answers the question: ⁠What happens if a variable is permanently changed starting in a given time-interval?

Details

Total effects are taken from the Leontief matrix \mathbf{(I-P)^{-1}}, where \mathbf{P} is the path matrix across variables and times. \mathbf{(I-P)}^{-1} \mathbf{\delta} calculates the effect of a perturbation represented by vector \mathbf{\delta} with length n_{\mathrm{lags}} \times n_{\mathrm{J}} where n_{\mathrm{J}} is the number of variables. \mathbf{(I-P)}^{-1} \mathbf{\delta} calculates the total effect of a given variable (from) upon any other variable (to) either in the same time (t=0), or subsequent times (t \geq 1), where \mathbf{\delta} = \mathbf{i}_{\mathrm{T}} \otimes \mathbf{i}_{\mathrm{J}}, where \mathbf{i}_{\mathrm{J}} is one for the from variable and zero otherwise. For a pulse experiment, \mathbf{i}_{\mathrm{T}} is one at t=0 and zero for other times. For a press experiment, \mathbf{i}_{\mathrm{T}} is one for all times.

We compute and list the total effect at each time from time t=0 to t=n_lags-1. For press experiments, this includes transient values as the the total effect approaches its asymptotic value (if this exists) as t approaches infinity. If the analyst wants an asymptotic effect from a press experiment, we recommend using a high lag (e.g., n_lags = 100) and then confirming that it has reached it's asymptote (i.e., the total effect is almost identical for the last and next-to-last lag), and then reporting the value for that last lag.

Value

A data frame listing the time-lag (lag), variable that is undergoing some exogenous change (from), and the variable being impacted (to), along with the total effect (total_effect) including direct and indirect pathways, and the partial "direct" effect (direct_effect)

Examples

### EXAMPLE 1
# Define linear model with slope of 0.5
sem = "
  # from, to, lag, name, starting_value
  x -> y, 0, slope, 0.5
"
# Build DSEM with specified value for path coefficients
mod = dsem(
  sem = sem,
  tsdata = ts(data.frame(x=rep(0,20),y=rep(0,20))),
  control = dsem_control( run_model = FALSE )
)

# Show that total effect of X on Y from pulse experiment is 0.5 but does not propagate over time
pulse = total_effect(mod, n_lags = 2, type = "pulse")
subset( pulse, from=="x" & to=="y")


### EXAMPLE 2
# Define linear model with slope of 0.5 and autocorrelated response
sem = "
  x -> y, 0, slope, 0.5
  y -> y, 1, ar_y, 0.8
"
mod = dsem(
  sem = sem,
  tsdata = ts(data.frame(x=rep(0,20),y=rep(0,20))),
  control = dsem_control( run_model = FALSE )
)

# Show that total effect of X on Y from pulse experiment  is 0.5 with decay of 0.8 for each time
pulse = total_effect(mod, n_lags = 4, type = "pulse")
subset( pulse, from=="x" & to=="y")

# Show that total effect of X on Y from press experiment  asymptotes at 2.5
press = total_effect(mod, n_lags = 50, type = "press")
subset( press, from=="x" & to=="y")

dsem documentation built on Sept. 16, 2025, 9:10 a.m.