# Tagged Questions

Causal inference tries to quantify the effect of a change in $X$ on $Y$ whilst holding constant or eliminating all other relevant factors which might influence this relationship.

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### Does causation imply correlation?

Correlation does not imply causation, as there could be many explanations for the correlation. But does causation imply correlation? Intuitively, I would think that the presence of causation means ...
21k views

### Under what conditions does correlation imply causation?

We all know the mantra "correlation does not imply causation" which is drummed into all first year statistics students. There are some nice examples here to illustrate the idea. But sometimes ...
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### Can cross validation be used for causal inference?

In all contexts I am familiar with cross-validation it is solely used with the goal of increasing predictive accuracy. Can the logic of cross validation be extended in estimating the unbiased ...
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### Statistics and causal inference?

In his 1984 paper "Statistics and Causal Inference", Paul Holland raised one of the most fundamental questions in statistics: What can a statistical model say about causation? This led to his ...
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### Criticism of Pearl's theory of causality

In the year 2000, Judea Pearl published Causality. What controversies surround this work? What are its major criticisms?
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### What's the relation between hierarchical models, neural networks, graphical models, bayesian networks?

They all seem to represent random variables by the nodes and (in)dependence via the (possibly directed) edges. I'm esp interested in a bayesian's point-of-view.
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### How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter?

I admit I'm relatively new to propensity scores and causal analysis. One thing that's not obvious to me as a newcomer is how the "balancing" using propensity scores is mathematically different from ...
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### To what extent is the distinction between correlation and causation relevant to Google?

Context A popular question on this site is " What are common statistical sins?". One of the sins mentioned is assuming that "correlation implies causation..." link Then, in the comments with 5 ...
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### X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean?

X and Y are not correlated (-.01); however, when I place X in a multiple regression predicting Y, alongside three (A, B, C) other (related) variables, X and two other variables (A, B) are significant ...
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### From a statistical perspective, can one infer causality using propensity scores with an observational study?

Question: From the standpoint of statistician (or a practitioner), can one infer causality using propensity scores with an observational study (not an experiment)? Please, do not want to start a ...
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### What do “endogeneity” and “exogeneity” mean substantively?

I understand that the basic definition of endogeneity is that $$X'\epsilon=0$$ is not satisfied, but what does this mean in a real world sense? I read the Wikipedia article, with the supply and ...
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### Introduction to causal analysis

What are good books that introduce causal analysis? I'm thinking of an introduction that both explains the principles of causal analysis and shows how different statistical methods could be used to ...
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### Are mediation analyses inherently causal?

I am interested in testing a simple mediation model with one IV, one DV, and one mediator. The indirect effect is significant as tested by the Preacher and Hayes SPSS macro, which suggests the ...
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### What is the difference between effectiveness and efficacy in determining the benefit of therapy 'A' on condition 'B'?

The context of this question is within a health framework i.e. looking at one or more therapies in the treatment of a condition. It appears that even well respected researchers confuse the terms ...
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### Whether to use structural equation modelling to analyse observational studies in psychology

I've noticed this issue coming up a lot in statistical consulting settings and i was keen to get your thoughts. Context I often speak to research students that have conducted a study approximately ...
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### What are the main differences between Granger's and Pearl's causality frameworks?

Recently, I ran across several papers and online resources that mention Granger causality. Brief browsing through the corresponding Wikipedia article left me with the impression that this term refers ...
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### Does simple linear regression imply causation?

I know correlation does not imply causation but instead the strength and direction of the relationship. Does simple linear regression imply causation? Or is an inferential (t-test, etc.) statistical ...
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### Real examples of Correlation confused with Causation

I'm looking for specific, real cases in which a causal relationship was inappropriately inferred from evidence of a correlation. Specifically, I'm interested in examples that meet the following ...
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### Interpreting Granger causality test's results

I'm trying to educate myself on Granger Causality. I've read the posts on this site and several good articles online. I also came across a very helpful tool, the Bivariate Granger Causality - Free ...
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### Causality in microeconometrics versus granger causality in time-series econometrics

I understand the causality as used in microeconomics (in particular IV or regression discontinuity design) and also the Granger causality as used in time-series econometrics. How do I relate one with ...
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### How fair is it to use the word “predict” for (logistic) regression?

My understanding is that even regression does not give causality. It can only give association between y variable and x variables and possibly a direction. Am I correct? I've often found phrases ...
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### Do edges in directed acyclic graph represent causality?

I am studying Probabilistic Graphical Models, a book for self-study. Do edges in a directed acyclic graph (DAG) represent causal relations? What if I want to construct a Bayesian network, but I am ...
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### Online resources for philosophy of causation for causal inference

Can you recommend any books, articles, essays, online tutorials/courses, etc that would be interesting and useful for an epidemiologist/biostatistician to learn about the philosophy of ...
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### Choice of path weights in SEM conceptual model using openMx

I am reviewing the R package OpenMx for a genetic epidemiology analysis in order to learn how to specify and fit SEM models. I am new to this so bear with me. I am following the example on page 59 of ...
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### Why is using cross-sectional data to infer / predict longitudinal changes a Bad Thing?

I'm looking for a paper which I hope exists, but don't know if it does. It could be a set of case studies, and / or an argument from probability theory, about why using cross-sectional data to infer / ...
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### How do instrumental variables address selection bias?

I'm wondering how an instrumental variable addresses selection bias in regression. Here's the example I'm chewing on: In Mostly Harmless Econometrics, the authors discuss an IV regression relating ...
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### Properties of bivariate standard normal and implied conditional probability in the Roy model

Sorry for the long title, but my problem is quite specific and hard to explain in one title. I am currently learning about the Roy Model (treatment effect analysis). There is one derivation step at ...
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### Is it possible to have a variable that acts as both an effect modifier and a confounder?

Is it possible to have a variable that acts as both an effect (measurement) modifier and a confounder for a given pair of risk-outcome associations? I'm still a little unsure of the distinction. I've ...
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### Random assignment: why bother?

Random assignment is valuable because it ensures independence of treatment from potential outcomes. That is how it leads to unbiased estimates of the average treatment effect. But other assignment ...
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### Understanding d-separation theory in causal Bayesian networks

I am trying to understand the d-Separation logic in Causal Bayesian Networks. I know how the algorithm works, but I don't exactly understand why the "flow of information" works as stated in the ...
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### Interpretation of positive and negative beta weights in regression equation

I received this elementary question by email: In a regression equation am I correct in thinking that if the beta value is positive the dependent variable has increased in response to greater ...
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### How does one verify causation?

After we have shown that two quantities are correlated how do we infer that the relationship is causal? And furthermore which one causes what? Now in theory one can use a "random assignment" (whatever ...
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### Why use control variables in differences-in-differences?

I have a question on the differences-in-differences approach with the following standard equation: $$y= a + b_1\text{treat}+ b_2\text{post} + b_3\text{treat}\cdot\text{post} + u$$ where treat is a ...
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### What to conclude when you fail to find an association in an epidemiological study?

Normally when somebody finds an association in an epidemiological study people are quick to point out that it doesn't prove causality, that there are problems of missing co-founders, that it is at ...
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### Model suggestion

Could anyone give me hints as to a model framework that can be used in the following setting: The outcome A is dichotomous. I want to investigate the effect of a continuous variable B and a ...
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### How much can the “pyramid of evidence” be applied to economics and political sciences?

When trying to assess a validity of a claim relying on statistics, I was taught (in the school of epidemiology) that the scale to use is â€œthe pyramid of evidenceâ€œ However, when conducting a ...
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### Does adjusting for superfluous variables bias OLS estimates?

The usual textbook treatment of adjusting for superfluous variables in OLS states that the estimator is still unbiased, but may have larger variance (see, for example, Greene, Econometric Analysis, ...
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### Computing inverse probability weights — conditional (multivariate) density estimation?

The general version: I need to estimate $f(A | X)$ where $A$ and $X$ are continuous and multivariate. I'd rather do it nonparametrically because I don't have a good functional form in mind and ...
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### Confidence interval for average treatment effect from propensity score weighting?

I am trying to estimate the average treatment effect from observational data using propensity score weighting (specifically IPTW). I think I am calculating the ATE correctly, but I don't know how to ...
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### Is there a branch of statistics that tries to explain “why” the dataset has certain statistical properties?

Suppose I have a big dataset and I compute some statistical summary of it - e.g., the correlation of one dimension with another. I think a reasonable question to ask would be "what data points ...
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### Big Data vs multiple hypothesis testing?

Nate Silver in his excellent "The Noise and the Signal" warned that we are much in awe of Big Data. But, that Big Data predictions in many fields have been disastrous (financial markets and economics ...
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### How do you find causal relationships in data?

Lets say I have a table with columns "A", "B" Is there a statistical method to determine if "A" causes "B" to happen? One can't really use Pearson's r, because: it only tests the correlation ...
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### Representing interaction effects in directed acyclic graphs

Directed acyclic graphs (DAGs; e.g. Greenland, et al, 1999) are a part of a formalism of causal inference from the contrafactual interpretation of causality camp. In these graphs the presence of an ...
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### Who conjectured that every correlation is caused by causal mechanisms?

I remember reading about this conjecture in Causality (Pearl, 2000). It states that every dependency between random variables can be explained (or originates from) a purely causal model. Of course ...
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### Can I use Synthetic Control Method for Comparative Case Studies with survey data?

I'd like to assess the impact of an upcoming policy implementation, as measured by changes in questionnaire response to a Likert-scale question. I understand I could use a difference-in-difference ...
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### Permutation testing in multiply adjusted analyses

Has there been or is there a consensus about how permutation testing should be done in multiply adjusted regression analyses? I understand the notion of "iteratively permuting the outcome variable" so ...
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### Graphical models for correlation of random variables and prediction of hidden observations

I am studying about Graphical Models and I came up with a simple example but I am not sure which kind of technique (HMM, DGM, MRF) would be able to help me with that. Imagine we have three balls that ...
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### Causal identification and penalized splines

I just got a rejection from an economics journal. Among the reasons cited for rejection were: the benefits of using the semi-parametric method are not clearly brought out compared to ...
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 ...