Questions tagged [causality]

The relationship between cause and effect.

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Can causal relationships be inferred from a random effects panel model?

Can a causal relationship between two variables be inferred from a random effects panel model? I estimated the following one-way random effects (RE) panel model: $\mathrm{Gini}_{it} = \alpha + \beta \...
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Derivation of residual bivariate expression to find the value for a multiple linear regression coefficient

Could someone help me with this derivation? How do I get to this expression of $k$? $y_i=\beta_0+kT_i+\beta_1X_{1i}+...+\beta_kX_{ki}+u_i$ $k = \frac{Cov(Y_i, \tilde{T_i})}{Var(\tilde{T_i})}$ where $\...
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Finidng dataset for causal inference (and instrumental variables) where response is bivariate [closed]

I am looking for an appropriate dataset for my research paper, and I am hoping you can recommend some open data for this purpose. I want to show our novel theoretical methodology on some application (...
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Cyclic Graphs and Causal Models

I am currently working through the second edition of Pearl's book Causality: Models Reasoning and Inference. As far as I can tell, Pearl's emphasis on DAGs excludes some potentially valid sets of ...
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Does an endogenous variable bias the coefficient of the exogenous one?

We have the following model: $$ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \epsilon. $$ We know that: \begin{align*} \operatorname{Cov}(x_1, \epsilon) &\neq 0 \\ \operatorname{Cov}(x_2, \epsilon) &...
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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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Interaction terms and causal interpretation

I'm estimating the following model: $Y_{i,t} = \alpha_{0} + \alpha_{1}X^{1}_{i,t} + \alpha_{2}*T_{t} + \alpha_{3}X^{1}_{i,t}*T_{t} $ In which $T_{t}$ is the year treated as a continuous variable, tend ...
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Negative transfer entropy

By definition, transfer entropy cannot be negative. However, using the Kraskov estimator, negative values can be obtained. In general, should we take precautions to avoid getting negative values? How ...
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Meaning of multiple exposures in a DAG

I am working with DAGs as a way to do some causal modeling. I am using dagitty - both the website and the R package. I feel like I have a good grasp of most things related to confounding, adjustment ...
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How is backdoor criterion used in practice?

Is the backdoor criterion applicable only for "learning" in a causal model (i.e. for estimating the causal effects between variables) or must it also be used when running that model, as in ...
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Entropy balancing---how do we assess overlap?

I am familiar with propensity score weighting. I set up the propensity score model, and then generally check for balance and overlap in propensity score to ensure that assumptions are met. However, I'...
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Difference-in-differences if the control group is treated later

Would a difference-in-differences analysis still tell me something important if the control group was treated later in time? Or, would I be better off only restricting my analysis to the time frame up ...
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Causal mediation effect decomposition when you have multiple mediators

Suppose we have outcome variable $Y,$ one treatment $T,$ and two mediator variables, $M_{1}$ and $M_{2}.$ We write the structural model as: $$ Y=\beta_{0}+\beta_{1}T+\beta_{2}M_{1}+\beta_{3}M_{2}+\...
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Multiple mediators and interaction effects- causal mediation effect

Assume we have a structural equation system with treatment $T,$ mediator $1$ (discrete) and mediator $2$ (continuous). We write this as: $$ Y=\beta_{0}+\beta_{1}M_{1}+\beta_{2}M_{2}+\beta_{3}TM_{2}+\...
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Difference-in-differences length for pre and post period

For difference-in-differences, do we need to select same duration/length for Pre period compared to Post period? For example, if post period is 5 months, do we need to select pre period to be of 5 ...
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Why is SATE different to Treatment effect (difference in means)?

A question from Gelman - Regression & Other Stories. This one has me a bit stumped, I've reread sections of the chapter and I'm still not understanding why this is the case. I think the answer is ...
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Difference in means vs OLS regression coefficients

Suppose I have a data set where each row represents a test subject. There's a dependent variable (y) and two binary columns (x1, ...
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Seeking help identifying the right causal model for my research

I am conducting a quasi-experimental research where the treatment is of varying intensity. For e.g., to investigate the impact of CEO's transgression on the stock market behavior (hypothetical; not my ...
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Is propensity score matching out of favor? [duplicate]

I came across this post, which was largely nonsensical, but a respondent suggested the original poster follow up with two articles: Ho, D. E., Imai, K., King, G., & Stuart, E. A. (2007). Matching ...
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Causal Inference for experiment

I'm working through a textbook (Regression and Other Stories) and have come across a particular problem that I am having difficulty convincing myself I understand. I am specifically interested in part ...
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What justifies the multiplication step in the proof of the front-door adjustment?

$\newcommand{\doop}{\operatorname{do}}$ The proofs of the front-door adjustment that I've read take three steps: Show $P(M|\doop(X))$ is identifiable Show $P(Y|\doop(M))$ is identifiable Multiply the ...
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How to think about exclusion restriction in an over-identified IV setup?

If I have more instruments than endogenous regressors, let’s say two instruments for one endogenous regressor, my IV set up is ‘over-identified’. What does the exclusion restriction imply with more ...
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Dealing with competing events from a CI perspecrive

Suppose I am a company eager to get at the (causal) effect between age and the event of contract termination. However, people can also die instead of actively terminating a contract. This seems like a ...
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Parents in a directed acyclic graph vs a partial ancestral graph

In DAGs, parents are defined as follows: A is a parent of B if 'A -> B' edge is in the graph. In PAGs, there are mixed type of edges, so you can have A -> B, A o-> B. Obviously if A -> B,...
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Good example of a walk-through of the FCI algorithm to ensure all steps are done

The FCI algorithm is a common algorithm used for learning a Markov equivalence class of causal graphs from observational data. I am wondering if there are any good examples that walk through a causal ...
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Methods for evaluating a geo-experimental research design (DiD, CausalImpact or a third option?)

I'm doing my undergraduate thesis on an experimental design of the incrementality of clicks using Google Ads vs not using Google Ads. I've created a geo-experimental design, where I've made a split of ...
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Categorical and ordinal variables and one dependent discrete variable

Í have a dataset with two categorical variables: let's say "city type" (categorical) and "living crampedness" (ordinal), and one discrete dependent variable ("house square ...
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Regression discontinuity vs propensity score matching

I have recently read some pieces suggesting that regression discontinuity designs could be the best statistical approach for causal inference stemming from non-randomized studies (eg 1 and 2). However,...
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What is the positivity assumption required for matching and ATT estimand?

Does ATT estimand require a less stringent positivity assumption in matching? For example, if a small treated group is matched to a large control group, most of the control subjects will be discarded ...
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Comparison of IPTW and regression adjustment in causal inference

Please see the reproducible R code in the end. The simulated data is from section 4.1 in the paper "ipw: An R Package for Inverse Probability Weighting", where we have measurements in 1000 ...
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How to compute transfer entropy between different length time-series?

Is there a way to calculate transfer entropy between two time series having different lengths? Given two time series: $x=(x_1,x_2,\dotsc,x_n)$ $y=(y_1,y_2,\dotsc,y_m)$, where $n \ne m$. Is there a way ...
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Assumptions in causal machine learning

I am currently reading about causal machine learning, e.g. causal bayesian networks. I am wondering about the assumptions on that the causal machine learning models are based. For example, for linear ...
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Identification of the transition probability of a time homogeneous MDP with subsampling

I am dealing with a MDP (or a temporal causal SEM) problem with missing observations. I want to know under what assumptions the transition probability can be identified from the observation. ...
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the causal factors in a subtracting relationship in directed acyclic graph

I have one variable A which is derived from subtracting C from B, i.e., A=B-C, does that mean B and C are both the causal factors of A if depicted in A DAG?
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Interpreting Logistic Regression Coefficients Under Collinearity

I thought this would be an easy question to find an answer to, but for the life of me I am having trouble finding anything that fully addresses my current problem: Consider a situation where we are ...
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Difference-in-difference covariates affecting outcome but failing parallel trends

I am performing a difference-in-difference analysis and, as advised by this post, ran my regression with each of my covariates as the outcome. I did this for each covariate individually using the ...
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Causal discovery with structured unobserved confounders and proxy variables

I face a problem of causal discovery with latent confounders. Unlike latent variables dealt in FCI (the Fast Causal Inference algorithm), the latent confounders in my problem are known to have some ...
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Addressing parallel trends violation Diff in Diff

I am analyzing the impact of a tax policy, and when I run the conventional DiD model, I see that there is a negative and statistically negative effect of 1.9. But when I visually checked pre-...
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Algorithm to check if there is an inducing path between two nodes - constructing maximal ancestral graph (MAG) given a DAG

In causal inference, one generally learns a Markov equivalence class of causal graphs when trying to reconstruct causal structure from data. This is known as a maximal ancestral graph (MAG). I am ...
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Targeted Learning in Data Science: background material

I am interested in the use of modern causal inference methods to research the association between a (non-genetic) exposure, and endogenous molecules and/or health outcomes (high-dimensional data). I ...
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Inverse Propensity Score Weighting vs. Double Machine Learning

I am familiar with Inverse Propensity Weighting (IPW) for the estimation of causal effects, and recently, I came across the 2016 paper by Chernozhukov et al. on Double/Debiased Machine Learning. From ...
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How to interpret a regression with both time and individual fixed effects?

Let's say we have the following regression $Y = \alpha + \beta X + \gamma W + u$ the way I interpret $\beta$ is "the effect of $X$ on $Y$ keeping $W$ constant". Now let's say that I have ...
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Expectation of Difference in Means estimator

Given i.i.d. observations $(Y_i, X_i)$ where $Y_i$ is the response and $X_i$ is binary valued, the difference in means estimator is $$ \hat{\theta} = \frac{1}{n_0} \sum_{i=1, X_i=0} Y_i - \frac{1}{n_1}...
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Is there any way of making a causation matrix, much like the correlation matrix?

So I have a bunch of parameters say $X_i \in \mathbb{X}$, where $i\in \{0,1,2...N\}$ . Now, I can find the correlation between any two features $i,j$ and get a matrix $\mathbb{C} = \text{Corr}(X,X)$. ...
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Multivariate transfer entropy

I have a set of time series to treat as sources and a time series to treat as destination. From the definition of multivariate transfer entropy, it seems to me that it can only be defined on two ...
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Difference between potential outcome and outcome conditioned on treatment

I'm reading up on Rubin causal inference and haven't been able to find a clear distinction between a potential outcome and the outcome conditioned on treatment, although this distinction is supposed ...
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Is there any theory or field of study that concerns itself with modeling causation rather than correlation?

My understanding is that probability (at least from a frequentist viewpoint) is a mathematical tool for modeling correlations. So, for example, we can say that two events $X$ and $Y$ are defined to be ...
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How reliable is conclusion drawn out from a known data?

Most of time conducting experiment is expensive. Suppose I and my collaborator decided to use a known databank(NHANE, NCI's data) to do some digging with some untested hypothesis given. Most of time ...
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DAG: what is the type of variable that only influences exposure?

What is the type of the left variable if this is not an instrument or conditional instrument? Is it just a covariate? Moderator?
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Explain variable influence of time series

Assumed I have a table of the following time series format: Snap_Date Dep_Date Route Bookings current_weather Days_before_departure DoW_Dep 0 2022-03-13 00:00:00 2022-05-01 00:00:00 JFK-ORD 1 cloudy ...
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