Test d-separation in a UMG

Reads a conditional-independence claim off the diagram by the d-separation criterion. Covariance edges are treated as latent common causes (the projection of an acyclic directed mixed graph onto a DAG), so that an unanalysed association behaves as a fork. The test generalises the vanishing-tetrad reasoning of the factor-analytic tradition and supplies the model's testable implications.

Usage

umg_dsep(model, x, y, given = character(0))

Arguments

model

An object of class umg.

x, y

Vertex names whose separation is queried.

given

Character vector of conditioning vertices (default none); may not contain x or y.

Value

TRUE if x and y are d-separated given given, FALSE otherwise.

Details

The test is carried out by the moralized ancestral graph criterion (Lauritzen, Dawid, Larsen, & Leimer, 1990), which is exact and runs in time linear in the size of the graph, so dense diagrams (for example, saturated network models) are handled without approximation.

Examples

m <- umg_mediation(direct = FALSE)
umg_dsep(m, "X", "Y")             # FALSE: connected through M
#> [1] FALSE
umg_dsep(m, "X", "Y", given = "M")  # TRUE: blocked by M
#> [1] TRUE