Depicting deterministic variables within directed acyclic graphs (DAGs): An aid for identifying and interpreting causal effects involving tautological associations, compositional data, and composite variables

TL;DR

This paper introduces a method to depict deterministic variables within DAGs, enhancing the interpretation of causal effects in compositional data, composite variables, and tautological associations.

Contribution

It proposes a two-step approach for representing deterministic variables in DAGs, improving clarity in causal inference involving complex variable relationships.

Findings

Easier identification of tautological associations

Improved understanding of conditioning on 'whole' variables in compositional data

Enhanced scrutiny of assumptions in composite variables

Abstract

Deterministic variables are variables that are fully explained by one or more parent variables. They commonly arise when a variable has been algebraically constructed from one or more parent variables, as with composite variables, and in compositional data, where the 'whole' variable is determined from its 'parts'. This article introduces how deterministic variables may be depicted within directed acyclic graphs (DAGs) to help with identifying and interpreting causal effects involving tautological associations, compositional data, and composite variables. We propose a two-step approach in which all variables are initially considered, and an explicit choice is then made whether to focus on the deterministic variable(s) or the determining parents. Depicting deterministic variables within DAGs bring several benefits. It is easier to identify and avoid misinterpreting tautological associations, i.e., self-fulfilling associations between variables with shared algebraic parent variables. In compositional data, it is easier to understand the consequences of conditioning on the 'whole' variable, and correctly identify total and relative causal effects. For composite variables, it encourages greater consideration of the target estimand and greater scrutiny of the consistency and exchangeability assumptions. DAGs with deterministic variables are a useful aid for planning and interpreting analyses involving tautological associations, compositional data, and/or composite variables.