causaleffect (version 1.3.15)

recover: Recover a causal effect from selection bias

Description

This function attempts to recover the causal effect of the set of variables (y) given the intervention on the set of variables (x) in graph (G) containing a single selection variable. Otherwise an error is thrown describing the graphical structure that witnesses non-identifiability. The vertex of (G) that corresponds to the selection variable must have a description parameter of a single character "S" (shorthand for "selection"). 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

recover(y, x, G, expr = TRUE, simp = TRUE, 
  steps = FALSE, primes = FALSE, stop_on_nonid = TRUE)

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.

Arguments

y

A character vector of variables of interest given the intervention.

x

A character vector of the variables that are acted upon.

G

An igraph object describing a causal model with a single selection variable in 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.

stop_on_nonid

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

Author

Santtu Tikka

References

Bareinboim E., Tian J. 2015 Recovering Causal Effects From Selection Bias. In Proceedings of the 29th AAAI Conference on Artificial Intelligence, 3475--3481.

See Also

parse.graphml, get.expression, generalize, meta.transport

Examples

library(igraph)

# We set simplify = FALSE to allow multiple edges.
g <- graph.formula(W_1 -+ X, W_2 -+ X, X -+ Y, # Observed edges
  W_2 -+ S, # The selection variable S
  W_1 -+ W_2, W_2 -+ W_1, W_1 -+ Y, Y -+ W_1, simplify = FALSE)

# Here the bidirected edges are set to be unobserved in the selection diagram d.
# This is denoted by giving them a description attribute with the value "U".
# The first five edges are observed, the rest are unobserved.
g <- set.edge.attribute(g, "description", 5:8, "U")

# The variable "S" is a selection variable. This is denoted by giving it
# a description attribute with the value "S".
g <- set.vertex.attribute(g, "description", 5, "S")

recover(y = "Y", x = "X", G = g)