Questions tagged [causality]

The relationship between cause and effect.

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Before using CV-selected Regression model for Inference, shouldn't model performance be evaluated on unused test set?

I just came across a biokinesiology paper that used some Machine Learning methods, but I think there is a flaw in their methodology. The authors had data on stroke patients and used Lasso regression ...
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Structural equation and causal model in economics

Structural equations is a useful language for causal analysis in economics. In Causality Pearl (2009 cap 5) we can find the best discussion about this. My question: is possible to use the concept of ...
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115 views

Conterfactual estimation in machine learning model

There are various techniques to build counterfactual estimations of certain variables for linear models in observational studies. Some of those are based on comparing the change in the predicted ...
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362 views

Machine Learning for Causal Inference with Panel Data: Possible to combine ML estimators with additive/linear terms to derive diff-in-diff estimator?

My question is motivated by the following. First consider the non-panel case, where we have two groups, the treated group ($g=t$) and the comparison group ($g=c$), and are trying to estimate an ...
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774 views

How can I control for time-varying unobserved heterogeneity with panel data?

I'm just beginning to learn econometrics, and I just learned about the fixed effects estimator, and the first-difference estimator. It's quite straightforward that those techniques allow me to control ...
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Ranking of causal models

I remember seeing a paper that ranked causal statistical models, published by some research body, by quality in terms of generalizability or some similar facet(s). This would be a "hierarchy of ...
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5k views

reverse causality and endogeneity problems

I am trying to analyse the effect of the gender of a CEO (women vs. men) on a performance measure of two types of firms (Conglomerate: i.e diversified firms, and Stand alone: i.e not diversified firms)...
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What does “even if the evidence remains correlational” mean?

From The smart move: we learn more by trusting than by not trusting | Aeon Ideas: We find the same pattern in other domains. People who trust the media more are more knowledgeable about politics and ...
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456 views

Formal definition of random assignment

I am looking for a formal definition of random assignment. Let $\mathbf{Z}$ be a vector of treatment assignments in which each element is 0 (unit not assigned to treatment) or 1 (unit assigned to ...
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416 views

Conditional probability and causality

I would like to understand the link between conditional probabilities and causality. More precisely: Assume we have two variables $A=\{0,1\}$ and $B=\{0,1\}$ and we observe: $P(A=1|B=1)>P(A=1|B=0)...
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Controlling for confounding variables in linear mixed effects models (lmer)

I'm using lmer to test how multiple variables (in this case, treatment, species, and sex) influence avian behaviour. ...
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1answer
179 views

The Book of Why, Table 8.1, Counterfactuals example

I'm reading "The Book of Why" by Judea Pearl and I'm getting an answer for a problem that doesn't match what the book says. This is my first foray into Structural Causal Models and their use, so I ...
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570 views

In observational studies with propensity score matching, why is the ATT usually reported? Is the ATE usually not available?

In most propensity score literature on observational studies, the ATT is usually reported and sought after. However, the ATE is usually not reported and in some cases I've read papers that claim you ...
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Names for some canonical directed causal graphs/illustrations of some canonical causal relationships?

Certain names are used for structures or node relationships that appear in acyclic, directed graphs (DAGs). Often these DAGs are interpreted causally. Here's a partial list for relationships that ...
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Graphical and Statistical Tests for Robustness of Sharp RD

I'm doing sharp regression discontinuity design with my treatment variable $$ D_i = \begin{cases} 1 \enspace \quad \text{if $x_i \geq \overline{x}$} \\ 0 \quad \text{otherwise} \end{cases} $$ where $\...
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Mix of terms causation and dependence in 'book of why'?

In the 'book of why' he says: the listening pattern prescribed by the paths of the causal model usually results in observable patterns or dependencies in the data I don't understand, why he says &...
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1answer
442 views

Do I need to adjust OLS standard errors after matching?

Suppose I use propensity score matching to create a dataset of treatment and control observations. Then I run OLS regression with some covariates that were not necessarily included in the propensity ...
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495 views

Theory behind Targeted Maximum Likelihood Estimation (TMLE)

There are many fine how-to articles describing how to implement TMLE but they avoid the details of the underlying theory. I'm currently working my way through Targeted Learning: Causal Inference for ...
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260 views

How to form groups before randomizing the treatment assignment?

Consider the following example. You want to assess the effect of a new class program on educational outcomes relative to the old program. You have recruited $N$ subjects for a randomized control trial ...
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1k views

Difference between covariates and treatment confounders in propensity score matching

Here, I have the definition of a propensity score: Propensity score is defined as the conditional probability of assignment to a treatment given a vector of covariates including the values of all ...
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2answers
2k views

Independence vs Autocorrelation

In Section 3.2 of R. S. Tsay, Analysis of Financial Time Series, I read: The basic idea behind volatility study is that the series {r_t} is either serially uncorrelated or with minor lower order ...
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1answer
930 views

In causal inference in statistics, how do you interpret the consistency assumption in mathematical terms?

In causal inference, the consistency assumption states that there are no multiple versions of treatment. Specifically, for a potential outcome unit $Y_i$ and a binary treatment vector $\mathbf{Z}$, $...
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Does regression analysis measure cause and effect?

Does regression analysis measure cause and effect? If yes, then how? If no, then what is done? Please describe with an example.
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1answer
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Causal Inference After Feature Selection

I am interested in this forum's thoughts concerning the use of LASSO for feature selection in a high dimensional dataset and subsequent OLS regression to adjust for confounding on the most frequently ...
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What can I validly conclude about a variable that becomes significant and switches sign when other variables are included in the model?

I have a dataset dat where each row represents a soil sample, with independent variables chemical measurements a, ...
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3answers
168 views

Law of total probability and conditioning on multiple events

Pearl et al. "Causal Inference in Statistics: A Primer" (2016) p. 56-57 includes the following equations (I have omitted a subscript $_m$ to $P$ as it plays no role in my question): \begin{align} &...
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145 views

Linear regression to answer causal questions

At a news agency, I want to understand whether the number of breaking news infuence the number of citations other media make relative to the news agency. I do not measure citations of exact news, ...
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2k views

Granger causality and non-linear regression

I’m new to Granger Causality concept. I know that the “Granger causality” is a statistical concept of causality that is based on prediction. According to Granger causality, if a time series X "Granger-...
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2k views

How to write a regression equation with mediation?

For my master's thesis I am examining a mediated relationship. I need to write out the equation model, but do not know exactly how to do this. In my case I have four independent variables, one ...
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88 views

Why conditioning on past treatment in IPTW with time-varying treatments?

Inverse probability weights with time-varying treatments $A_t$ and confounders $L_t$ are defined as the inverse probability of being treated at time $t$ conditional on past treatment and covariate ...
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2answers
281 views

Using random effects to adjust for cluster-level confounding?

There is a usage of random intercepts to adjust for unobserved cluster-level confounding, as for example argued here: Are random effects confounding variables? How do random effects adjust for ...
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106 views

Causal Inference: Calculate Expectation

This question is from Kang&Schafer(2007), shown in the following picture: where $\pi_i$ is the propensity score function, i.e, $\mathrm{P}(T_i=1|Z_i=z_i)$. I am very confused how I can derive $r^{...
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4k views

SUTVA vs. independence

In the Wikipedia article on the Rubin causal model I stumbled upon the following quote: We require that "the [potential outcome] observation on one unit should be unaffected by the particular ...
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543 views

Correct and clear wording for non-causal correlation

Despite reading multiple statistics and epidemiology texts as well as studies, I have trouble describing the following in plain English for a public of doctors (so, non-statisticians or biomedical ...
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6k views

Formula for one-sided Hodrick-Prescott filter

I am not very familiar with filters. The Hodrick-Prescott filter as one can find it e.g. in wikipedia is two-sided. I also found an R implementation for this in the R package mFilter. There the filter ...
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1answer
303 views

Difference between an “Empirical Strategy” and an “Identification Strategy” in econometrics?

What are the substantive differences between these terms, specifically for economists? Are instrumental variables, difference-in-differences, and regression discontinuity designs considered ‘...
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1answer
113 views

Do-Calculus for Causal Diagram 7.5 from “The Book of Why” (napkin problem)

In "The Book of Why" the below causal diagram is described as the "simplest model" where estimation of the causal effect goes beyond front and back-door adjustment and thus ...
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1answer
92 views

Mediation: a & b path positive & significant, insignificant total effect and NEGATIVE direct effect

I am testing a mediation model for a research question using PROCESS in SPSS. While I realize Baron and Kenny (1986) would not test this model, I have read quite a bit about it not being necessary for ...
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1answer
255 views

Calculate single absolute standardized difference across levels of a categorical treatment variable cobalt::bal.tab

Can I calculate a single absolute standardized difference (ASD) across the levels of my categorical treatment variable? For reporting in a balance table. I performed an inverse probability of ...
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Is there an algorithm for listing all/minimum admissable sets in a graph that satisfies the backdoor criterion in Causal Inference?

I would like to know if there exists an algorithm for finding all/minimum admissible sets in a graph that satisfy the backdoor criterion as defined by Judea Pearl in his book Causality (Please see ...
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1answer
569 views

Measurment error for two variables

I am interested in estimating the effect of security S on crime C in a given city over time (eight quarters) for twenty cities, so it's panel data. The problem is, instead of actual security spending ...
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Choice of referent twin in twin difference model

Carlin (2005) points out that mixed effects models specifically for twin data can be simplified by calculating differences between paired clusters. This allows for modeling specifically the within ...
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1answer
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Where does this formula for the effect of the mediator on the outcome comes from?

I am reading the paper Caron, P.-O., & Valois, P. 2018. A computational description of simple mediation analysis. The Quantitative Methods for Psychology, 14(2): 147–158. There there is the ...
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Which one of these methods ATE, ATT, ATO (overlap) should be used to evaluate a strategically applied treatment?

Lets assume I have data from a medical trial in which a new medicine was given to patients who, based on certain characteristics, doctors believed that they would benefit from this new treatment. I ...
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Causality in correlations between multiple variables

Let's say I have 4 or 5 variables of interest which I measured for each of about 500 people. So, imagine a 500x5 matrix. Because of the nature of these variables, it is obvious that there must be (and ...
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1answer
367 views

What does “randomly assigned conditional on some observable” mean intuitively?

From my textbook it say that "If the treatment in a quasi-experiment is "as if" randomly assigned, conditional on some observed variables w, then the treatment effect can be estimated using ...
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142 views

In a randomized trial, what is the propensity score?

In Rosenbaum's 1983 paper, he states that "in a randomized trial, the propensity score is a known function so that there exists one accepted specification." I am wondering what this specification is ...
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61 views

Why use the “best model according to data” in academic research; wildly unrealistic? [closed]

When someone fits a GLM model, it is the "perfect" fit based on the algorithm. But I find that this is absurd... we are not looking for "the best model", we are looking for the correct one. Given ...
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144 views

Path Analysis in the Presence of a Conditioned-Upon Collider

In path analysis (i.e., DAGS as linear structural equation models), where all relationships between variables are assumed to be linear, you can compute the association between two variables by ...
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Difference-in-difference model with mediators: Estimating the effect of different elements of a policy

How do I conduct a mediation analysis in a difference-in-difference setting? For example, a city selects some neighborhoods for a new crime fighting strategy (the treatment $D$) that involves an ...

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