cfid: An R Package for Identification of Counterfactual Queries in Causal Models

Overview

This package facilitates the identification of counterfactual queries in structural causal models via the ID* and IDC* algorithms by Shpitser, I. and Pearl, J. (2007, 2008) https://arxiv.org/abs/1206.5294, https://jmlr.org/papers/v9/shpitser08a.html. A simple interface is provided for defining causal graphs and counterfactual conjunctions. Construction of parallel worlds graphs and counterfactual graphs is done automatically based on the counterfactual query and the causal graph.

For further information, see the tutorial paper on this package published in The R Journal: https://doi.org/10.32614/RJ-2023-053

Installation

You can install the latest development version by using the devtools package:

# install.packages("devtools")
devtools::install_github("santikka/cfid")

Graphs

Directed acyclic graphs (DAG) can be defined using the function dag in a syntax similar to the dagitty package. This function accepts edges of the form X -> Y, X <- Y, and X <-> Y, where the last variant is a shorthand for a latent confounder affecting both X and Y (a so-called bidirected edge). Subgraphs can be defined using curly braces {...}. Edges to and from subgraphs connect to all vertices present in the subgraph. Subgraphs can also be nested. Some examples of valid constructs include:

dag("X -> Y <- Z <-> W")
dag("{X Y Z} -> {A B}")
dag("X -> {Z <-> {Y W}}")

which define the following DAGs:

flowchart LR;
  X((X))-->Y((Y));
  Z((Z))-->Y;
  W((W))<-.->Z;

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flowchart LR;
  X((X))-->A((A));
  Y((Y))-->A;
  Z((Z))-->A;
  X-->B((B));
  Y-->B;
  Z-->B;

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flowchart LR;
  X((X))-->Z((Z));
  X-->Y((Y));
  X-->W((W));
  Z<-.->Y;
  Z<-.->W;

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Counterfactual variables and conjunctions

A counterfactual variable is defined by its name, value, and the submodel that it originated from (a set of interventions). For example, $y_x$ is a counterfactual variable named $Y$ with the value assignment $y$ that originated from a submodel where the intervention $do(X = x)$ took place.

The function counterfactual_variable and its shorthand alias cf can be used to construct counterfactual variables. This function takes three arguments: var, obs, and sub that correspond to the variable name, observed value assignment and subscript (the submodel). For example, $y_x$ is defined as follows:

cf(var = "Y", obs = 0, sub = c(X = 0))
#> y_{x}

by default, the value 0 is the “default” or baseline level, and integer values different from 0 are denoted by primes. For example $y'_x$ is a similar counterfactual variable to $y_x$, except that it was observed to take the value $y'$ instead of $y$ This can be accomplished by changing the obs argument:

cf(var = "Y", obs = 1, sub = c(X = 0))
#> y'_{x}

Purely observational counterfactual variables (of the original causal model) can be defined by omitting the sub argument.

Conjunctions of multiple counterfactual variables can be constructed using the function counterfactual_conjunction or its shorthand alias conj. This function simply takes an arbitrary number of "counterfacual_variable" objects as its argument. For example, the counterfactual conjunction $y \wedge y'_x$ can be defined as follows:

v1 <- cf("Y", 0)
v2 <- cf("Y", 1, c("X" = 0))
conj(v1, v2)
#> y /\ y'_{x}

Identification

Identifiability of (conditional) counterfactual conjunctions can be determined via the function identifiable. This function takes the conjunction gamma to be identified from the set of all interventional distributions $P_*$ of the causal model represented by the "dag" object g. An optional conditioning conjunction delta can also be provided. The solution is provided in LaTeX syntax if the query is identifiable. For instance, we can consider the identifiability of $P(y_x|x' \wedge z_d \wedge d)$ in the DAG shown below as follows:

flowchart TB;
  X((X))-->W((W));
  W-->Y((Y));
  D((D))-->Z((Z));
  Z-->Y;
  X<-.->Y;

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g1 <- dag("X -> W -> Y <- Z <- D X <-> Y")
v1 <- cf("Y", 0, c(X = 0))
v2 <- cf("X", 1)
v3 <- cf("Z", 0, c(D = 0))
v4 <- cf("D", 0)
c1 <- conj(v1)
c2 <- conj(v2, v3, v4)
identifiable(g = g1, gamma = c1, delta = c2)
#> The query P(y_{x}|x' /\ z_{d} /\ d) is identifiable from P_*.
#> Formula: \frac{\sum_{w} P_{x}(w)P_{w,z}(y,x')}{P(x')}

For more information and examples, please see the package documentation.

Related packages

• The causaleffect package provides the ID and IDC algorithms for the identification of causal effects (among other algorithms).
• The dosearch package provides a heuristic search algorithm that uses do-calculus to identify causal effects from an arbitrary combination of input distributions.
• The dagitty package provides various tools for causal modeling, such as finding adjustment sets and instrumental variables.
• The R6causal package implements an R6 class for structural causal models, and provides tools to simulate counterfactual scenarios for discrete variables.