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This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…

Methodology · Statistics 2026-05-21 Jiehan Liu , Ziyi Liu , Yiqing Xu

We propose semi- and non-parametric methods to estimate conditional interventional effects in the setting of two discrete mediators whose causal ordering is unknown. Average interventional indirect effects have been shown to decompose an…

Methodology · Statistics 2023-04-19 Max Rubinstein , Zach Branson , Edward H. Kennedy

A/B tests serve the purpose of reliably identifying the effect of changes introduced in online services. It is common for online platforms to run a large number of simultaneous experiments by splitting incoming user traffic randomly in…

Machine Learning · Computer Science 2022-10-18 Alexander Buchholz , Vito Bellini , Giuseppe Di Benedetto , Yannik Stein , Matteo Ruffini , Fabian Moerchen

The ability to answer causal questions is crucial in many domains, as causal inference allows one to understand the impact of interventions. In many applications, only a single intervention is possible at a given time. However, in some…

Machine Learning · Statistics 2022-10-12 Olivier Jeunen , Ciarán M. Gilligan-Lee , Rishabh Mehrotra , Mounia Lalmas

Contextual sensing and delivery of digital interventions to improve health outcomes have gained significant traction in behavioral and psychiatric studies. Micro-randomized trials (MRTs) are a common experimental design for obtaining…

Methodology · Statistics 2025-04-01 Jieru Shi , Zhenke Wu , Walter Dempsey

Causal mediation analysis can improve understanding of the mechanisms underlying epidemiologic associations. However, the utility of natural direct and indirect effect estimation has been limited by the assumption of no confounder of the…

Applications · Statistics 2020-06-16 Kara E. Rudolph , Oleg Sofrygin , Wenjing Zheng , Mark J. van der Laan

Good models require good training data. For overparameterized deep models, the causal relationship between training data and model predictions is increasingly opaque and poorly understood. Influence analysis partially demystifies training's…

Machine Learning · Computer Science 2024-04-02 Zayd Hammoudeh , Daniel Lowd

We introduce a double/debiased machine learning estimator for the impulse response function in settings where a time series of interest is subjected to multiple discrete treatments, assigned over time, which can have a causal effect on…

Econometrics · Economics 2025-12-17 Daniele Ballinari , Alexander Wehrli

This paper concerns robust inference on average treatment effects following model selection. In the selection on observables framework, we show how to construct confidence intervals based on a doubly-robust estimator that are robust to…

Statistics Theory · Mathematics 2018-04-13 Max H. Farrell

We consider repeated measurement designs when a residual or carry-over effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment…

Statistics Theory · Mathematics 2014-11-20 R. A. Bailey , P. Druilhet

We establish the inferential properties of the mean-difference estimator for the average treatment effect in randomized experiments where each unit in a population is randomized to one of two treatments and then units within treatment…

Statistics Theory · Mathematics 2019-02-19 Zach Branson , Tirthankar Dasgupta

The behavior of the conditional logistic estimator is analyzed under a causal model for two-arm experimental studies with possible non-compliance in which the effect of the treatment is measured by a binary response variable. We show that,…

Statistics Theory · Mathematics 2008-09-15 Francesco Bartolucci

This paper proposes a doubly robust two-stage semiparametric difference-in-difference estimator for estimating heterogeneous treatment effects with high-dimensional data. Our new estimator is robust to model miss-specifications and allows…

Econometrics · Economics 2020-09-08 Yang Ning , Sida Peng , Jing Tao

We present current methods for estimating treatment effects and spillover effects under "interference", a term which covers a broad class of situations in which a unit's outcome depends not only on treatments received by that unit, but also…

Applications · Statistics 2020-01-16 Peter M. Aronow , Dean Eckles , Cyrus Samii , Stephanie Zonszein

Mediation analysis has become a widely used method for identifying the pathways through which an independent variable influences a dependent variable via intermediate mediators. However, limited research addresses the case where mediators…

Methodology · Statistics 2025-06-10 Rui Ren , Haoyi Yang , Qian Xiao , Lingzhou Xue , Yuan Huang

We investigate how to learn treatment effects away from the cutoff in multiple-cutoff regression discontinuity designs. Using a microeconomic model, we demonstrate that the parallel-trend type assumption proposed in the literature is…

Econometrics · Economics 2025-09-03 Yuta Okamoto , Yuuki Ozaki

Attrition in survey and field experiments presents a challenge for social science research. Common approaches to deal with this problem -- such as complete case analysis, multiple imputation, and weighting methods -- rely on strong…

Methodology · Statistics 2026-04-13 Xiangyu Song

The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…

Statistics Theory · Mathematics 2022-01-19 Tomas Masak , Soham Sarkar , Victor M. Panaretos

Psychological interventions, especially those leveraging mobile and wireless technologies, often include multiple components that are delivered and adapted on multiple timescales (e.g., coaching sessions adapted monthly based on clinical…

This letter introduces several doubly, triply, and quadruply robust estimators of the controlled direct effect. Among them, the triply and quadruply robust estimators are locally semiparametric efficient, and well suited to the use of…

Methodology · Statistics 2020-11-20 Xiang Zhou