Estimate a total causal effect in a VARMA-LiNGAM model

Estimates the total causal effect from from_index (optionally at lag from_lag) to to_index (at the current time) using the fitted VARMA-LiNGAM model. Port of the Python reference estimate_total_effect: the destination variable is regressed on the source variable together with the source's parents (a back-door adjustment) over lagged X and lagged residual regressors, and the source's coefficient is returned.

Usage

estimate_varma_total_effect(X, result, from_index, to_index, from_lag = 0)

Arguments

X

original data (matrix or data frame), rows ordered in time; must be the data the model was fitted on (the residuals stored in result are aligned to it)

result

a VARMALiNGAMResult from lingam_varma()

from_index

source variable (1-based index or variable name)

to_index

destination variable (1-based index or variable name)

from_lag

lag of the source variable (0 = current time, default)

Value

the estimated total effect (scalar)

Details

The Python reference requires the residual matrix E as an argument; here it is reconstructed internally from result$residuals and the fitted instantaneous matrix B0, so only the original data are needed.

Examples

sample <- generate_varmalingam_sample(n = 1000, seed = 42)
model <- lingam_varma(sample$data,
  order = c(1, 1), criterion = NULL,
  reg_method = "ols", prune = FALSE
)

# total effect of x0 (current) on x2 (current)
estimate_varma_total_effect(sample$data, model, from_index = 1, to_index = 3)
#> [1] -0.2569613