causal.effect: Identify a causal effect

Description

This function returns an expression for the joint distribution of the set of variables (y) given the intervention on the set of variables (x) conditional on (z) if the effect is identifiable. Otherwise an error is thrown describing the graphical structure that witnesses non-identifiability. If steps = TRUE, returns instead a list where the first element is the expression and the second element is a list of the intermediary steps taken by the algorithm.

Usage

causal.effect(y, x, z = NULL, G, expr = TRUE, simp = FALSE, 
  steps = FALSE, primes = FALSE, prune = FALSE, stop_on_nonid = TRUE)

Arguments

A character vector of variables of interest given the intervention.

A character vector of the variables that are acted upon.

A character vector of the conditioning variables.

An igraph object describing the directed acyclic graph induced by the causal model that matches the internal syntax.

expr

A logical value. If TRUE, a string is returned describing the expression in LaTeX syntax. Else, a list structure is returned which can be manually parsed by the function get.expression.

simp

A logical value. If TRUE, a simplification procedure is applied to the resulting probability object. d-separation and the rules of do-calculus are applied repeatedly to simplify the expression.

steps

A logical value. If TRUE, returns a list where the first element corresponds to the expression of the causal effect and the second to the a list describing intermediary steps taken by the algorithm.

primes

A logical value. If TRUE, prime symbols are appended to summation variables to make them distinct from their other instantiations.

prune

A logical value. If TRUE, additional steps are taken to remove variables that are not necessary for identification.

stop_on_nonid

A logical value. If TRUE, an error is produced when a non-identifiable effect is discovered. Otherwise recursion continues normally.

Value

If steps = FALSE, A character string or an object of class probability that describes the interventional distribution. Otherwise, a list as described in the arguments.

References

Shpitser I., Pearl J. 2006 Identification of Joint Interventional Distributions in Recursive semi-Markovian Causal Models. Proceedings of the 21st National Conference on Artificial Intelligence, 2, 1219--1226.

Shpitser I., Pearl J. 2006 Identification of Conditional Interventional Distributions. Proceedings of the 22nd Conference on Uncertainty in Artificial Intelligence, 427--444.

Examples

Run this code

# NOT RUN {
library(igraph)

# simplify = FALSE to allow multiple edges
g <- graph.formula(x -+ y, z -+ x, z -+ y , x -+ z, z -+ x, simplify = FALSE)

# Here the bidirected edge between X and Z is set to be unobserved in graph g
# This is denoted by giving them a description attribute with the value "U"
# The edges in question are the fourth and the fifth edge
g <- set.edge.attribute(graph = g, name = "description", index = c(4,5), value = "U")
causal.effect("y", "x", G = g)

# Pruning example
p <- graph.formula(x -+ z_4, z_4 -+ y, z_1 -+ x, z_2 -+ z_1, 
  z_3 -+ z_2, z_3 -+ x, z_5 -+ z_1, z_5 -+ z_4, x -+ z_2, z_2 -+ x, 
  z_3 -+ z_2, z_2 -+ z_3, z_2 -+ y, y -+ z_2,
  z_4 -+ y, y -+ z_4, z_5 -+ z_4, z_4 -+ z_5, simplify = FALSE)
p <- set.edge.attribute(p, "description", 9:18, "U")
causal.effect("y", "x", G = p, primes = TRUE, prune = TRUE)

# Simplification example
s <- graph.formula(x -+ y, w -+ x, w -+ z, z -+ y)
causal.effect("y", "x", G = s, simp = FALSE)
causal.effect("y", "x", G = s, simp = TRUE)
# }