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)
```

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 the conditioning variables.

G

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.

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) # }