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.
causal.effect(y, x, z = NULL, G, expr = TRUE, simp = FALSE,
steps = FALSE, primes = FALSE, prune = FALSE, stop_on_nonid = TRUE)
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.
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
.
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.
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.
A logical value. If TRUE
, prime symbols are appended to summation variables to make them distinct from their other instantiations.
A logical value. If TRUE
, additional steps are taken to remove variables that are not necessary for identification.
A logical value. If TRUE
, an error is produced when a non-identifiable effect is discovered. Otherwise recursion continues normally.
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.
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.
# 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) # }