A package for storing and simulating data for causal inference in Julia.
Causal inference is the process of estimating, from data, the effect of a treatment variable on an outcome variable -- typically in the presence of confounders. CausalTables.jl makes it easier to store, process, and simulate datasets involving causal structure. Specifically, the package provides:
- A
CausalTabledata structure that wraps any dataset stored in a Tables.jl-compatible format with a causal structure (i.e. labeling treatment, response, confounders, and other variables). - Utility methods for easily extracting relevant causal variables and applying interventions.
- A
StructuralCausalModeldata structure for generating random datasets endowed with a given causal structure. - Methods to computing true conditional distributions and approximate ground truth causal effect estimands.
When used together, these functionalities make it easier to implement new causal inference methods in Julia, as well as randomly generate data to evaluate their performance against the ground truth in simulation studies.
CausalTables.jl can be installed using the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run
Pkg> add CausalTables
To simulate data, one must first define a StructuralCausalModel (SCM). An SCM is composed of a DataGeneratingProcess, which is a sequence of random variables, along with labels for treatment, response, and confounder variables. For example, the following code defines an SCM with a binary treatment @dgp macro constructs a DataGeneratingProcess object according to the simple syntax name ~ distribution, where rhs is a Distribution object from Distributions.jl. More advanced syntax is detailed in the documentation.
using CausalTables
using Distributions
dgp = @dgp(
W ~ Beta(2, 4),
A ~ (@. Bernoulli(W)),
Y ~ (@. Normal(A + W, 1))
)
scm = StructuralCausalModel(dgp; treatment = :A, response = :Y, confounders = [:W])
Once a StructuralCausalModel is defined, one can then draw a randomly-generated CausalTable according to the SCM using the rand function:
ctbl = rand(scm, 100)
CausalTable
┌───────────┬───────┬───────────┐
│ W │ A │ Y │
│ Float64 │ Bool │ Float64 │
├───────────┼───────┼───────────┤
│ 0.381527 │ true │ 0.809227 │
│ 0.576206 │ true │ 3.22163 │
│ 0.380546 │ false │ 1.70505 │
│ 0.226648 │ false │ 0.185022 │
│ ⋮ │ ⋮ │ ⋮ │
│ 0.385836 │ false │ -0.392848 │
│ 0.204554 │ false │ 0.638084 │
│ 0.232177 │ true │ 0.832707 │
│ 0.0465189 │ false │ 1.29168 │
└───────────┴───────┴───────────┘
92 rows omitted
Summaries: NamedTuple()
Arrays: NamedTuple()
A CausalTable is a Table with a causal structure, such as labels for treatment, response, and confounder variables. In addition to implementing the standard Tables.jl interface, CausalTables.jl also provides extra functions to make working with causal data easier. See the documentation for more information.
Given an SCM, it is also possible to approximate the "ground truth" value of a variety of relevant causal estimands from this SCM, including counterfactual means (cfmean), as well as average treatment effects (ate) and average policy effects (ape). For example, the ground truth average treatment effect for this SCM can be approximated like so:
ate(scm)
(μ = 1.0006736394005957, eff_bound = 2.0019300075151616)
Alternatively, one can compute the ground truth of low-level statistical functionals, such as conditional means or propensity scores, for use in downstream analyses.
propensity(scm, ctbl, :A)
100-element Vector{Float64}:
0.17900559797871887
0.653489070854697
⋮
0.8247576289722464
See the documentation for more information and tutorials.
If you find a bug, have a feature request, or otherwise experience any issues with this software package, please open an issue on the issue tracker. If you would like to contribute code to the software yourself, we encourage you to open a pull request. We welcome all contributions, including bug fixes, documentation improvements, and new features.