Causal Inference for Circular Data

TL;DR

This paper extends causal inference methods to circular data, introducing new treatment effects for direction and length, with estimators validated through simulations and applied to real-world dispatcher sleep pattern data.

Contribution

It proposes novel causal effect measures (ADTE and ALTE) for circular data and develops estimators with strong theoretical properties.

Findings

Estimators show ideal theoretical properties in simulations.

Application to dispatcher data reveals significant effects of job types.

Method effectively captures causal effects on circular outcomes.

Abstract

In causal inference, a fundamental task is to estimate the effect resulting from a specific treatment, which is often handled with inverse probability weighting. Despite an abundance of attention to the advancement of this task, most articles have focused on linear data rather than circular data, which are measured in angles. In this article, we extend the causal inference framework to accommodate circular data. Specifically, two new treatment effects, average direction treatment effect (ADTE) and average length treatment effect (ALTE), are introduced to offer a proper causal explanation for these data. As the average direction and average length describe the location and concentration of a random sample of circular data, the ADTE and ALTE measure the change in direction and length between two counterfactual outcomes. With inverse probability weighting, we propose estimators that exhibit ideal theoretical properties, which are validated by a simulation study. To illustrate the practical utility of our estimator, we analyze the effect of different job types on dispatchers' sleep patterns using data from Federal Railroad Administration.