# 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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### 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 ...
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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### 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 ...
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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 ...
390 views

### Transfer function in forecasting models - interpretation

I am occupied with ARIMA modelling augmented with exogenous variables for promotional modelling purposes and i have hard time explaining it to business users. In some cases software packages end up ...
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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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### 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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### Is there evidence of mediation? Need help with interpretation of mediation analysis results

I have performed a mediation analysis. I have an independent variable T, a mediator M, and outcome Y. (All 3 variables are binary, and I use logit.) (While I used Stata ...
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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'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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### 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 ...
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### What test is this for endogenous variables?

Can somebody tell me whether the following R code (for econometrics endogenous variables) is for a Hausman test, a Nakamura test, or some other test? ...
18k 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 ...
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### What test should I use to determine if a policy change had a statistically significant impact on website registrations?

A client's website was operating under a certain policy for membership sign ups for over a year. At the start of October 2012 the client implemented a new policy for sign ups that was supposed to ...
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### Omitted Variable Bias, verification in Gretl

I am trying to verify the expression for Omitted Variable Bias (OVB) as given e.g. in Wooldridge: $\tilde{\beta_1} = \hat{\beta_1} + \hat{\beta_2} \cdot \tilde{\delta_1}$, where $\tilde{\delta_1}$ is ...
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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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### 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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### Can two linear regression variables be perfectly correlated but not share a single causal chain ancestor?

A causal chain lists event (or fact) $y$ with all its causal antecedents. We make a model of the following form: $$y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \epsilon$$ $\hat\beta_1$ has a p-value ...
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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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### 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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### 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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### 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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### 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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### 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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### What are the best empirical studies comparing causal inference with experimental, quasi-experimental, and non-experimental techniques?

The Issue: People attempt to draw causal inferences using many different statistical techniques (e.g. regression, propensity score matching, regression discontinuity, instrumental variables, etc.). ...
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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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### 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 ...
214 views

### Infer causality with high collinearity

I recently started to ask myself how to measure the impact of education on indexes like GDP: what is the outcome of mathematics or computer science on GDP, at the country level for instance. In this ...
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### 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: ...
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### Must there be “an effect to be mediated” in mediational analysis (i.e., must IVs & DVs be correlated)?

Baron and Kenny outlined several steps to aid in determining if a mediational analysis is appropriate to test a particular hypothesis. The very first step was "Show that the initial [independent] ...
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### Does rejection of null hypothesis in multiple regression entail causation?

We make a model of the following form: $$y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \epsilon$$ and with $n=1,000$, $\hat\beta_1$ has a p-value <0.001. If our data and data collection meets ...
635 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 an IV regression relating ...
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### How to test whether correlation measures differ when controlling or not for a third variable?

If the correlation between demographic dissimilarity and satisfaction is $r=.-14$ and the partial correlation, with career development partialled out, between demographic dissimilarity and ...
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### How wise is the use of ANCOVA when groups differ on the covariate?

In this case I presume loss of ANCOVA power, so I donĀ“t know what type of analysis should I run next. There was significant difference in covariate between groups (p=0,008). Is there some solution? ...
269 views

### 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 ...
286 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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### 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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### Causality studies on observational data: DID with 2SLS to compliment Rubin causal model

A study with observational data has treatment and control group but the assignment is not randomised: some chose to be in the treament, some otherwise. But the choice had been made before the ...
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### Correlation versus cause-effect regression

I know correlation does not imply causation. I have read it nth time. (i.e. weight does not cause height etc. etc.) However, to find the effect of a moderator variable on X-Y relationship, a ...
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### Proving Causality with t-test/regression

Earlier today I was discussing statistical analysis software with a colleague of mine. My colleague had primarily used SPSS in previous work for performing t-tests, anovas, manovas, and other ...
Given a joint probability distribution over the variables $X_1,X_2,\dots,X_n$. Is there an algorithm for constructing the corresponding Bayesian Network?