Heather Battey’s contribution to the Discussion of ‘Parameterizing and simulating from causal models’ by Evans and Didelez
本文提出了一种节俭参数化方法，以因果效应为中心构建模型，支持从参数化因果分布中模拟和进行似然推断，适用于离散和连续变量。
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.