meta.transport {causaleffect} R Documentation

## Derive a transport formula for a causal effect between a target domain and multiple source domains

### Description

This function returns an expression for the transport formula of a causal effect between a target domain and multiple source domains. The formula is returned for the interventional distribution of the set of variables (`y`) given the intervention on the set of variables (`x`). The multiple source domains are given as a list of selection diagrams (`D`). If the effect is non-transportable, an error is thrown describing the graphical structure that witnesses non-transportability. The vertices of any diagram in (`D`) that correspond to selection variables must have a description parameter of a single character "S" (shorthand for "selection").

### Usage

```meta.transport(y, x, 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. `D` A list of `igraph` objects describing the selection diagrams 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 transport formula 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.

Santtu Tikka

### References

Bareinboim E., Pearl J. 2013b Meta-Transportability of Causal Effects: A Formal Approach. Proceedings of the 16th International Conference on Artificial Intelligence and Statistics, 135–143.

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

### Examples

```library(igraph)

# Selection diagram corresponding to the first source domain.
# We set simplify = FALSE to allow multiple edges.
d1 <- graph.formula(X -+ Z, W_1 -+ W_2, W_2 -+ Z,
W_3 -+ Z, X -+ W_3, W_2 -+ X, Z -+ Y, # Observed edges
S_1 -+ X, S_2 -+ W_2, S_3 -+ W_3, S_4 -+ Y, # Edges related to selection variables
X -+ W_3, W_3 -+ X, X -+ W_2, W_2 -+ X, X -+ W_1,
W_1 -+ X, W_1 -+ Z, Z -+ W_1, simplify = FALSE)

# Here the bidirected edges are set to be unobserved in the selection diagram d1.
# This is denoted by giving them a description attribute with the value "U".
# The first 7 edges are observed and the next 4 are related to the selection variables.
# The rest of the edges are unobserved.
d1 <- set.edge.attribute(d1, "description", 12:19, "U")

# The variables "S_1", "S_2", "S_3" and "S_4" are selection variables.
# This is denoted by giving them a description attribute with the value "S".
d1 <- set.vertex.attribute(d1, "description", 7:10, "S")

# Selection diagram corresponding to the second
# source domain is constructed in a similar fashion.
d2 <- graph.formula(X -+ Z, W_1 -+ W_2, W_2 -+ Z, W_3 -+ Z,
X -+ W_3, W_2 -+ X, Z -+ Y, # Observed edges
S_1 -+ X, S_2 -+ W_2, S_3 -+ W_1,
S_4 -+ Y, S_5 -+ Z, # Edges related to selection variables
X -+ W_3, W_3 -+ X, X -+ W_2, W_2 -+ X, X -+ W_1,
W_1 -+ X, W_1 -+ Z, Z -+ W_1, simplify = FALSE)
d2 <- set.edge.attribute(d2, "description", 13:20, "U")
d2 <- set.vertex.attribute(d2, "description", 7:11, "S")

# We combine the diagrams as a list.
d.comb <- list(d1, d2)
meta.transport(y = "Y", x = "X", D = d.comb)
```

[Package causaleffect version 1.3.13 Index]