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In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…

Methodology · Statistics 2021-05-04 Xingguo Wu

In animal behavior studies, a common goal is to investigate the causal pathways between an exposure and outcome, and a mediator that lies in between. Causal mediation analysis provides a principled approach for such studies. Although many…

A common goal in comparative effectiveness research is to estimate treatment effects on pre-specified subpopulations of patients. Though widely used in medical research, causal inference methods for such subgroup analysis remain…

Assessing causal effects in the presence of unobserved confounding is a challenging problem. Existing studies leveraged proxy variables or multiple treatments to adjust for the confounding bias. In particular, the latter approach attributes…

Methodology · Statistics 2023-10-17 Yong Wu , Mingzhou Liu , Jing Yan , Yanwei Fu , Shouyan Wang , Yizhou Wang , Xinwei Sun

Estimating causal effects from observational data (at either an individual -- or a population -- level) is critical for making many types of decisions. One approach to address this task is to learn decomposed representations of the…

Machine Learning · Computer Science 2021-11-15 Negar Hassanpour , Russell Greiner

Meta-analysis is commonly used to combine results from multiple clinical trials, but traditional meta-analysis methods do not refer explicitly to a population of individuals to whom the results apply and it is not clear how to use their…

Mediation analysis aims to identify and estimate the effect of an exposure on an outcome that is mediated through one or more intermediate variables. In the presence of multiple intermediate variables, two pertinent methodological questions…

Quantitative Methods · Quantitative Biology 2026-01-06 Allan Jérolon , Flora Alarcon , Florence Pittion , Magali Richard , Olivier François , Etienne E. Birmelé , Vittorio Perduca

Causal inference for air pollution mixtures is an increasingly important issue with appreciable challenges. When the exposure is a multivariate mixture, there are many exposure contrasts that may be of nominal interest for causal effect…

Methodology · Statistics 2024-02-01 Joseph Antonelli , Corwin Zigler

Using observed language to understand interpersonal interactions is important in high-stakes decision making. We propose a causal research design for observational (non-experimental) data to estimate the natural direct and indirect effects…

Computation and Language · Computer Science 2021-09-17 Katherine A. Keith , Douglas Rice , Brendan O'Connor

We consider modeling a binary response variable together with a set of covariates for two groups under observational data. The grouping variable can be the confounding variable (the common cause of treatment and outcome), gender,…

Methodology · Statistics 2023-04-13 Rasool Tahmasbi , Keyvan Tahmasbi

We investigate the estimation of the causal effect of a treatment variable on an outcome in the presence of a latent confounder. We first show that the causal effect is identifiable under certain conditions when data is available from…

Artificial Intelligence · Computer Science 2025-06-16 Yaroslav Kivva , Sina Akbari , Saber Salehkaleybar , Negar Kiyavash

Unobserved confounding is a major hurdle for causal inference from observational data. Confounders---the variables that affect both the causes and the outcome---induce spurious non-causal correlations between the two. Wang & Blei (2018)…

Machine Learning · Statistics 2019-05-31 Yixin Wang , David M. Blei

Mediation analysis seeks to understand the mechanism by which a treatment affects an outcome. Count or zero-inflated count outcome are common in many studies in which mediation analysis is of interest. For example, in dental studies,…

Methodology · Statistics 2016-07-12 Zijian Guo , Dylan S. Small , Stuart A. Gansky , Jing Cheng

Causal mediation analysis is complicated with multiple effect definitions that require different sets of assumptions for identification. This paper provides a systematic explanation of such assumptions. We define five potential outcome…

Methodology · Statistics 2022-09-26 Trang Quynh Nguyen , Ian Schmid , Elizabeth L. Ogburn , Elizabeth A. Stuart

Causal inference from observational data often assumes "ignorability," that all confounders are observed. This assumption is standard yet untestable. However, many scientific studies involve multiple causes, different variables whose…

Machine Learning · Statistics 2019-04-16 Yixin Wang , David M. Blei

Mediation analysis has traditionally focused on outcome-level summary contrasts, such as mean effects, which may obscure substantial distributional changes induced by complex and nonlinear causal mechanisms. We propose Distributional Causal…

Machine Learning · Statistics 2026-05-05 Jinlun Zhang , Haoneng Huang , Zishu Zhan , Chunquan Ou

A fundamental task in science is to determine the underlying causal relations because it is the knowledge of this functional structure what leads to the correct interpretation of an effect given the apparent associations in the observed…

Artificial Intelligence · Computer Science 2024-08-02 Alexandre Trilla , Nenad Mijatovic

Estimation of heterogeneous treatment effects is an active area of research. Most of the existing methods, however, focus on estimating the conditional average treatment effects of a single, binary treatment given a set of pre-treatment…

Methodology · Statistics 2025-05-30 Max Goplerud , Kosuke Imai , Nicole E. Pashley

Fields like public health, public policy, and social science often want to quantify the degree of dependence between variables whose relationships take on unknown functional forms. Typically, in fact, researchers in these fields are…

Statistics Theory · Mathematics 2019-12-10 Octavio César Mesner , Cosma Rohilla Shalizi

We introduce a novel framework for decomposing interventional causal effects into synergistic, redundant, and unique components, building on the intuition of Partial Information Decomposition (PID) and the principle of M\"obius inversion.…

Artificial Intelligence · Computer Science 2025-09-22 Abel Jansma