Skip to contents

Converts total effects to direct effects and visa verse

Source: R/total_to_direct.R
total_direct_conversion.Rd

Assuming a matrix of total linear effects W we can convert this to a matrix of direct effects W_dir This assume that W_tot = W_dir + W_dir^2 + W_dir^3 + ... We can solve for W_dir = I - (I + W_tot)^-1 assume that the spectral radius (largest absolute eigenvalue) of W_dir < 1 This condition is the same that abs(eigenvalue(W_tot) / (1 + eigenvalue(W_tot))) < 1

Usage

total_to_direct(W, restrict_dag = TRUE, enforce_spectral_radius = TRUE)

direct_to_total(W, restrict_dag = TRUE)

Arguments

W

A matrix of total/direct linear effects

restrict_dag

A boolean indicating if the matrix must be a directed acyclic graph

enforce_spectral_radius

A boolean indicating if the spectral radius of W_dir must be less than 1. Generally not recommended to disable

Value

A matrix of direct effects

Examples

B <- matrix(c(0, 0.6, -0.5, 0), nrow = 2, byrow = TRUE)
total_to_direct(B,  restrict_dag = F)
#>            [,1]      [,2]
#> [1,]  0.2307692 0.4615385
#> [2,] -0.3846154 0.2307692
all(zapsmall(direct_to_total(total_to_direct(B, restrict_dag = F), restrict_dag = F)) == B)
#> [1] TRUE

B2 <- matrix(c(0,0,0,
             1,0,0,
             1,1,0), nrow = 3, byrow = TRUE)
total_to_direct(B2)
#>      [,1] [,2] [,3]
#> [1,]    0    0    0
#> [2,]    1    0    0
#> [3,]    0    1    0