# Questions tagged [counterfactuals]

An *if* statement in which the condition is untrue or unrealized. Used in causal analysis for comparing potential outcomes under different hypothesized conditions.

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### How to interpret the conditional expectation mean $E[Y(0)\mid Z=1]$ where $Y(0)$ is the potential outcome on control and $Z$ the treatment assignment?

How can I interpret the conditional expectation mean $E[Y(0)\mid Z=1]$ where $Y(0)$ is the potential outcome on control and $Z$ the treatment assignment? I believe it is the "expected outcome if ...
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### Average treatment effect: counterfactual and graphical derivation

I have some (shameful) doubts about the Average Treatment Effect (ATE), also known as Average Causal Effect (ACE). In this setting, I am interested in a binary exposure/treatment variable ...
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### Impact of counterfactual hiring decisions

As the hiring manager for my widget company, in order to decide whether to progress an applicant to an interview I administer an IQ test. If the applicant's score is above 110 on the test I let them ...
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### How can I compute a counterfactual query for discrete binary variables?

In computing counterfactual queries for structural causal models (SCMs), J. Pearl says to go through 3 steps. Abduction Action Prediction In his book, Causal Inference in Statistics, he shows how to ...
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### AB Testing with and without counterfactuals

My boss wants us to run a simple experiment where we manipulate the search results on our website. He is insisting that we must have counterfactuals for the results to be valid. The way I see ...
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### Significance of pie-charts in representing sufficient-cause components

In the book Causal Inference - What If, the authors present a form of pie-chart-type diagram to represent sufficient-cause components (refer to figure 5.1 on page 64 and figure 5.2 on page 65 ...
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### Why have both standardization and IP weighting, when they are fundamentally similar?

In Causal Inference: What If by Hernan and Robins, I came across two methods to find causal effect - standardization (page 19) and IP weighting (page 20). It seems both methods are fundamentally same. ...
1 vote
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### Variable selection in causal inference regression models when $p > n$?

Are there accepted techniques for selecting variables in causal inference (not prediction) where the number of variables exceeds our sample size, making a standard OLS regression impossible? Assume ...
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### Creating deliberate missing data to impute a counter factual

This question is more out of curiosity than necessity. Any useful resources/literature will be massively appreciated. Recently started research in a new field that I’m unfamiliar with: economic policy ...
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### Clarification Needed on Derivation in Judea Pearl's "Detecting Latent Heterogeneity" (2015)

I'm reading a paper by Judea Pearl titled "Detecting Latent Heterogeneity" from 2015, which can be found at this link: Detecting Latent Heterogeneity I'm having trouble understanding a ...
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### Noise abduction for computing counterfactuals

Given observational data $X$ and knowledge of the true causal graph structure $\mathcal{G}$. How does abduction of the exogenous noise ($U$) for computing counterfactuals work? We don't have data ...
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### How to convert a Gamma GLM to a Pearl's Structural Causal Model (SCM) with exogenous noise terms?

Assume both X and Y are univariate for this. So in Judea Pearl's SCM, you have endogenous variables and exogenous noise. A regular causal Bayesian Network like X->Y where X and Y|X is normal can be ...
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### Question about using potential outcomes in DAGs in real world example

I am trying to understand how DAGs and potential outcomes look together. I came across these excellent posts (here and here, but I am trying to understand how this looks in a real world example. ...
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### In a diff-in-diff or regression discontinuity research design, why is it important to describe why the counterfactual is a plausible one?

I've heard it mentioned that in difference-in-differences, regression discontinuity, or even in some other quasi-experimental research designs, that the counterfactual should be explained as a ...
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### Counterfactual Bayesian survival analysis in pymc

I am trying to determine mortality rates for untreated patients from an observational dataset where treatment has occurred (thus blocking the possibility of further untreated mortality). You can't ...
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### Matching on pre-treatment outcome $z$-score in diff-in-diff analysis to avoid regression toward the mean bias in $ATT$ estimates?

There have been many articles (e.g., Chabé-Ferret (2017), Daw & Hatfield (2018), Zeldow & Hatfield (2021)) discussing the perils of matching on pre-treatment outcomes (such as patient's ...
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### Should inverse probability weighting be used in two-way fixed-effects panel regression?

Let's assume a (balanced) panel data set with two measurement points $t_0$ and $t_1$, where $t_0$ may be considered as the baseline. Some of the ID's are treated at $t_1$, i.e. $D=1$, the assignment ...
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### Conditional exchangeability when conditioning on continuous variable

Conditional exchangeability is often introduced in a simple setting with a binary outcome, binary treatment, and binary confounding variable. In this setting, exchangeability holds within strata of ...
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### Textbook recommendations covering machine learning techniques for causal inference?

Over the past 15 years there has been progress in adapting machine learning methods for causal inference. For example: targeted learning, double machine learning, causal trees. Is there a textbook ...
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### Counterfactual Estimation - Common Practices in Applied Causality

I am quite new to the topic and trying to figure out a workflow for causal analysis. My aim is to establish a baseline of ATE (I think) and then experiment with disentangled representations and ...
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### Constrastive vs Counterfactual Explanations

Is there any canonical definition for Contrastive vs Counterfactual explanations? In the literature, I keep reading different versions but I wonder if there are good definitions or illustrative ...
1 vote
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### Correct methodology using $g$-computation to estimate Average Treatment Effect on the Treated ($ATT$)?

I have a question about the $g$-computation methodology for estimating the Average Treatment Effect on the Treated ($ATT$) in the following article. The authors recommend estimating the $ATT$ by first ...
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### Generalized DiD with non-binary treatment variable? How to proceed?

I have a certain law as my (non-binary) treatment variable (range: 0-2) at the state level which takes on different values based on whether it prohibits altogether (2), limits (1), or allows the ...
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### The average treatment effect and the difference in means

Hi I have a question related to the treatment effect. Recently, I am reading literatures on treatment effect and have a question. In the literatures, we denote the counterfactual outcomes as $Y_1$ and ...
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### Using counterfactual modeling techniques to assess racial bias in predictive models

My team at a health insurance company is discussing how we might measure racial bias in the various predictive models our company uses to assess future health risk (such as annual medical cost or ...
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### Linear model: potential outcome framework vs. structural causal model

From my reading about the potential outcomes framework (POF) and structural causal models (SCM), I understand that both perspectives have been shown to be equivalent but take different starting points....
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### find upper and lower bounds on average causal effect $\theta$

I am working on some problems in All of statistics by Wasserman, and I am not quite sure how to tackle this problem. Suppose you are given data $(X_1, Y_1), \dots, (X_n, Y_n)$ from an observational ...
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### Strong ignorability: confusion on the relationship between outcomes and treatment

In the research area of potential outcomes and individual treatment effect (ITE) estimation, a common assumption called ''strong ignorability'' is often made. Given a graphical model with the ...
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### Difference between the counterfactual mean and average treatment effect

I am new on the causality topic, I don't know the difference between the average treatment effect and counterfactual mean. Can anyone tell me?
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### Instrumental variables: In which cases would the average treatment effect on the treated (ATT) and local average treatment effect (LATE) be similar?

It seems that if the proportion of always-takers in the control group (to whom eligibility was not assigned) is much smaller than the proportion of compliers in the treatment group (to whom ...
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### Adjustment formula for counterfactuals: can we get rid of $X=x$?

Pearl et al. "Causal Inference in Statistics: A Primer" (2016) p. 108 contains the following adjustment formula (based on the backdoor criterion) for probabilities of counterfactuals expressed using ...
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### Counterfactual Expectation Calculation

$\newcommand{\doop}{\operatorname{do}}$ Problem: (This is from Study question 4.3.1 from Causal Inference in Statistics: A Primer, by Pearl, Glymour, and Jewell.) Consider the causal model in the ...
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### How can I update a disease prediction model with new treatment group data while maintaining the original causal relationships?

Context: I have a prediction model which predicts the probability of getting a disease. This prediction model has been created based on data of patients who did not get any form of treatment. I use ...
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### How to understand probability of Necessity (PN) ≥ 100%, as in this example from 'Causal Inference in Statistics a primer'

In the book 'Causal Inference in Statistics A Primer' By Pearl et al. there is an example towards the end, (Ex 4.5.1 page 119) that calculates the probability of necessity PN = 1, and the authors ...
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### Counterfactuals in Econometric Modeling (Abortion-Crime Hypothesis Revisited)

Donohue and Levitt (2019) recently published a working paper revisiting the abortion-crime link. My question is specific to equation (2) in their paper (see below):  ln(CRIME_{st}) = \beta_{1}...
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### What are counterfactual objectives?

What is a simple-to-understand definition/explanation for counterfactual objectives in Machine Learning? I heard this term in this 3 minutes paper presentation https://youtu.be/TOpJ4g9v-H4.
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### Offline evaluation of Counter factual data for Recommendation

I am building new model and facing at offline evaluation tasks. My goal is to predict higher CTR(=click/impression) advertisement, and improve sales.(sales would improve if user watch more ...
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### The counterfactual model for causation

My professional training took place in the late 1990's and I don't recall hearing some of the terminology that seems nigh-universal nowadays. I believe the accepted name is "counterfactual model for ...
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