Normalize latent structure in a DAG

Normalizes a DAG with latent variables while preserving the induced marginal model over the observed variables. This is done by:

(1) exogenizing all latent nodes (making them parentless), (2) removing exogenous latent nodes with at most one child, and (3) removing exogenous latent nodes whose child sets are strict subsets of another latent node's child set.

This corresponds to Lemmas 1–3 in Evans (2016).

Usage

normalize_latent_structure(cg, latents)

Arguments

cg

A caugi object of class "DAG".

latents

Character vector of latent node names.

Value

A caugi object of class "DAG".

References

Evans, R. J. (2016). Graphs for margins of Bayesian networks. Scandinavian Journal of Statistics, 43(3), 625–648. doi:10.1111/sjos.12194

See also

Other operations: condition_marginalize(), dag_from_pdag(), exogenize(), latent_project(), meek_closure(), moralize(), mutate_caugi(), skeleton()

Examples

dag <- caugi(
  A %-->% U,
  U %-->% X + Y,
  class = "DAG"
)

normalize_latent_structure(dag, latents = "U")
#> <caugi object; 4 nodes, 4 edges; simple: TRUE; session=0x555e332d26c0>
#>   graph_class: DAG
#>   nodes: A, U, X, Y
#>   edges: A-->X, A-->Y, U-->X, U-->Y

# More complex example with two latents and nested child sets
dag2 <- caugi(
  A %-->% U,
  U %-->% X + Y + Z,
  U2 %-->% Y + Z,
  class = "DAG"
)
normalize_latent_structure(dag2, c("U", "U2"))
#> <caugi object; 5 nodes, 6 edges; simple: TRUE; session=0x555e3120d970>
#>   graph_class: DAG
#>   nodes: A, U, X, Y, Z
#>   edges: A-->X, A-->Y, A-->Z, U-->X, U-->Y, U-->Z