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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6answers
14k views

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 ...
42
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14answers
9k 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 ...
27
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7answers
1k views

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 ...
24
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3answers
1k views

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 ...
21
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2answers
595 views

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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3answers
422 views

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 ...
16
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2answers
1k views

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.
13
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4answers
2k views

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 ...
13
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2answers
260 views

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 ...
13
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4answers
4k views

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 ...
11
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3answers
5k views

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 ...
11
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4answers
8k views

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 ...
11
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1answer
237 views

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 ...
9
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2answers
2k views

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 ...
8
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4answers
30k views

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 ...
8
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1answer
159 views

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 ...
8
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3answers
579 views

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 ...
8
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1answer
117 views

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 ...
7
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1answer
419 views

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 ...
6
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4answers
168 views

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 ...
6
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2answers
8k views

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 ...
6
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4answers
1k views

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 ...
6
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3answers
187 views

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 ...
6
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1answer
386 views

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 “the pyramid of evidence“ However, when conducting a ...
5
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3answers
3k views

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 ...
5
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1answer
4k views

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 ...
5
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1answer
73 views

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 and IV regression relating ...
5
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1answer
83 views

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 ...
5
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3answers
399 views

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 ...
5
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3answers
111 views

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 ...
5
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1answer
1k views

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 ...
5
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2answers
188 views

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 ...
5
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1answer
72 views

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 ...
5
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1answer
120 views

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 ...
4
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3answers
249 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 ...
4
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1answer
154 views

Are the relations in fixed, random and mixed effect models and multilevel models causal?

In fixed, random and mixed effect models, and multilevel models, the response random variable is represented as a function of some explanatory variables and random errors. I was wondering if the ...
4
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2answers
314 views

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.
4
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3answers
424 views

Fuzzy regression discontinuity design and exclusion restriction

In a fuzzy regression discontinuity design, what does the exclusion restriction look like in terms of a conditional expectation between the instrument in the first stage and the error term in the ...
4
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2answers
138 views

Difference-in-Differences Estimator for Logistic Regressions

I have a pre-post intervention study with four groups: 1) Pre-Intervention Control, 2) Pre-Intervention Treatment, 3) Post-Intervention Control, and 4) Post-Intervention Treatment. The outcome is a ...
4
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1answer
118 views

Why arrange variables by causality in bivariate regression?

Suppose we have variables $(X,Y)$ and we have theory tell us that $X$ $\overset{\text{cause}}{\implies} Y$. Perhaps they're time-series variables and it would be common to see something like this: ...
4
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2answers
179 views

Causation implication

I recently read an article about how you can increase longevity by sleeping less. This article, like many others I've read, references a statistical study and implies that causation was found between ...
4
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3answers
450 views

Can causality be inferred in a study with an experience followed by two sets of measures

I came across this study as part of a mock exam paper and was confused to say the least. Context: The study investigates cognitive and behavioural factor related to the experience of anxiety in MRI ...
3
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3answers
218 views

Mathematical definition of causality

Let $Y$ and $X$ be random variables. $E(Y|X)$ is the conditional mean of $Y$ given $X$. We say $Y$ is not causally related to $X$ if $E(Y|X)$ does not depend on $X$, which implies it is equal to ...
3
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2answers
100 views

What to do in logistic regression if you have a huge amount of variables?

I am dealing with logistic regression, trying to identify variables which have a causal relationship with a binary response. The way I usually do it is to try variables one by one and visualize the ...
3
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2answers
6k views

Difference between experimental data and observational data?

I'm a novice to data mining and started to read about it. What's the exact difference between experimental data and observation data? Both are obviously data; and many say observation data can lead to ...
3
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2answers
515 views

Differentiating correlation and causation using conditional probablity

I'm trying to understand the difference between causation and correlation using conditional probabilities. From what I understand, one may quantify causation by $P(E_1|E_2) / P(E_1)$. For example, ...
3
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3answers
466 views

Identifying the time lag between cause and effect

What approaches exist to observe the time lag between two variables? I need to analyze the relationship between blood pressure and some other factor, such as exercise. The data set I am drawing from ...
3
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3answers
671 views

How much sub-questions impact one ordinal question in a survey

I have a variable NPS which is an item on a survey, the answer format is ordinal, 0 to 10. Then there are sub-questions on the same survey, some are ordinal, some are categorical. I would like to ...
3
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2answers
255 views

How do difference-in-difference designs account for temporal autocorrelation

Although there are doubtless many techniques for studying the impact of a discrete intervention over time, I am interested in two which have achieved widespread adoption in the social sciences: ...
3
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1answer
569 views

How to test for causation in a static panel data model with small t?

I have a static panel data model with small T (T=5) that makes it impossible for me to use granger causality as it requires a long time span. So my question: Is there any alternative solution to ...