Parameterizing and Simulating from Causal Models

TL;DR

This paper introduces a new 'frugal parameterization' method centered on causal effects, enabling easier construction, simulation, and likelihood-based inference of causal models, including Bayesian approaches.

Contribution

It proposes a novel parameterization framework focused on causal effects, facilitating model construction, simulation, and inference for both discrete and continuous variables.

Findings

Allows construction of models with specified causal distributions

Enables simulation from the models for causal inference

Supports likelihood-based and Bayesian inference methods

Abstract

Many statistical problems in causal inference involve a probability distribution other than the one from which data are actually observed; as an additional complication, the object of interest is often a marginal quantity of this other probability distribution. This creates many practical complications for statistical inference, even where the problem is non-parametrically identified. In particular, it is difficult to perform likelihood-based inference, or even to simulate from the model in a general way. We introduce the `frugal parameterization', which places the causal effect of interest at its centre, and then builds the rest of the model around it. We do this in a way that provides a recipe for constructing a regular, non-redundant parameterization using causal quantities of interest. In the case of discrete variables we can use odds ratios to complete the parameterization, while in the continuous case copulas are the natural choice; other possibilities are also discussed. Our methods allow us to construct and simulate from models with parametrically specified causal distributions, and fit them using likelihood-based methods, including fully Bayesian approaches. Our proposal includes parameterizations for the average causal effect and effect of treatment on the treated, as well as other causal quantities of interest.