Whether a pair forms a bow

NOT LOCATED IN THE EXTRACTED TEXT of the corpus copy of Molak. The definition and theorem are taken from the primary source: "A bow-arc is a pair of variables, one of which is a direct function of the other, whose error terms are correlated"; "Theorem 4. (Brito and Pearl, 2002b) (Bow-free Rule) Every acyclic model whose path diagram lacks bow-arcs is identified." – Chen, B. and Pearl, J. (2015), Graphical Tools for Linear Structural Equation Modeling, UCLA Technical Report R-432, p. 15, citing Brito, C. and Pearl, J. (2002), Structural Equation Modeling 9(4):459-474. identified reports Theorem 4 itself: acyclic AND bow-free.

Usage

morie_bowarc(dag, bidirected, x, y)

Arguments

dag

directed edge matrix

bidirected

two-column matrix of bidirected edges

x, y

the ordered pair to test

Value

list(isbow, direct, confounded, nbows, bowfree, acyclic, identified, bows)

Examples

morie_bowarc(dag = c(1, 2, 3, 4, 5, 6, 7, 8), bidirected = c(1, 2, 3, 4, 5, 6, 7, 8),
  x = c(1, 2, 3, 4, 5, 6, 7, 8), y = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $isbow
#> [1] FALSE
#> 
#> $direct
#> [1] FALSE
#> 
#> $confounded
#> [1] FALSE
#> 
#> $nbows
#> [1] 0
#> 
#> $bowfree
#> [1] TRUE
#> 
#> $acyclic
#> [1] TRUE
#> 
#> $identified
#> [1] TRUE
#> 
#> $bows
#> character(0)
#>