transport {causaleffect}

Derive a transport formula for a causal effect between two domains

Description

This function returns an expression for the transport formula of a causal effect between two domains. The formula is returned for the interventional distribution of the set of variables (y) given the intervention on the set of variables (x) in a selection diagram (D). If the effect is non-transportable, an error is thrown describing the graphical structure that witnesses non-transportability. The vertices of (D) that correspond to selection variables must have a description parameter of a single character "S" (shorthand for "selection"). By default, every variable is available for intervention in the source. If only a subset of the variables is available, then the set (z) can be used to derive specific z-transportability.

Usage

transport(y, x, z = NULL, D, expr = TRUE, simp = TRUE, 
  steps = FALSE, primes = FALSE, stop_on_nonid = TRUE)

Arguments

y

A character vector of variables of interest given the intervention.

x

A character vector of the variables that are acted upon.

z

A character vector of variables available for intervention. NULL value corresponds to ordinary transportability.

D

An igraph object describing a selection diagram 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.

Value

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

Author(s)

Santtu Tikka

References

Bareinboim E., Pearl J. 2013a A General Algorithm for Deciding Transportability of Experimental Results. Journal of Causal Inference, 1, 107–134.

Bareinboim E., Pearl J. 2013c Causal Transportability with Limited Experiments. Proceedings of the 27th AAAI Conference on Artificial Intelligence, 95–101.

See Also

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

Examples

library(igraph)

# We set simplify = FALSE to allow multiple edges.
d <- graph.formula(X -+ Z, Z -+ W, W -+ V, V -+ Y, S -+ V, # Observed edges
  X -+ Z, Z -+ X, V -+ Y, Y -+ V, X -+ Y, Y -+ X, 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.
d <- set.edge.attribute(d, "description", 6:11, "U")

# The variable "S" is a selection variable. This is denoted by giving it
# a description attribute with the value "S". 
d <- set.vertex.attribute(d, "description", 6, "S")

transport(y = "Y", x = "X", D = d)