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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Estimating the probability of causation based on finding a correlation, including experimental details

Say there is a hypothesis that A causes B (A -> B), and some likelihood that the hypothesis is correct (AB1%). Now, an experiment is run that claims to find a correlation between A and B. What I ...
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2k 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 ...
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80 views

Estimating a confidence interval around the average of an interacted treatment effect

I've got a causal inference situation with heterogeneous treatment effects. In addition to simply estimating coefficients, I'd like to get an average effect of the treatment at the covariate values ...
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65 views

causal inference with correlated multivariate outcomes

I've been struggling with how to think about the causal estimate of a program on two outcomes, when one of the two outcomes affects the other outcome. It seems sort of like simultaneous equations, ...
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39 views

Guessing test question answers from scores

My teacher likes to give online quizzes that are about 20-30 questions long. Every student has the same questions in the same order. We are not told after taking the quiz which questions we got wrong, ...
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1answer
53 views

Average causal effect of one year increase in schooling vs a four-year increase in schooling

I'm not sure why in Mostly Harmless Econometrics, last paragraph of p. 55, the expectations of $f_{i}(s-4)$ is taken and the expectation of $f_{i}(s-1)$ is not. The text reads: Conditional on ...
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3answers
144 views

How to rule out double causation

I have a model where I suspect (purely on theoretical grounds) that double causation might be an issue. How can I test this hypothesis? I.e. I have something like $Y_i = \beta_0 + \beta_1 X_i + ...
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1answer
74 views

Why is the conditional mean of the reduced form error zero?

For example, we have a simultaneous equation model of supply and demand: Supply: $$s(p)=\alpha_{s}+\beta_{s}p+\epsilon_{s}$$ Demand: $$d(p)=\alpha_{d}-\beta_{d}p+\epsilon_{d}$$ Market clearing ...
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1answer
95 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 ...
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1answer
50 views

How to refer to variables which lie beyond causal pathway

Causal diagrams are extremely good tools for discussing research plans for multivariate modeling between statisticians and non-statisticians. It's easy after some deliberation to decide which ...
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1answer
181 views

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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2answers
120 views

Correlation or t-test?

Following experimental design was done and some data as shown in table below was obtained: pretest> intervention1> intervention2> posttest > perception survey Number of students=60 Number of ...
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184 views

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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1answer
142 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 ...
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2answers
119 views

Does randomization really allow us to make claims of causality?

Lets say two groups are compared. Subjects are randomly assigned to each group, then a treatment is given to half while a placebo is given to the other half. All aspects of the experiment (order of ...
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1answer
135 views

Two highly correlated variables where both correlate with a third: Correlation and Causation

My question is certainly quite basic for statisticians! Let's suppose Var1 and Var2 are highly correlated with a poor $R^2$. ...
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1answer
160 views

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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1answer
69 views

Interpretation of lasso recovery results

When people say that lasso regression can under certain assumptions recover "the support", i.e. non-zero regression weights, what does this mean? This cannot mean causal recovery, because Pearl has ...
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667 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 ...
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102 views

Causality in Time Series

I am reading an article which is trying to justify the need for causal inference in their inferential framework. The thought experiment is as follows: Suppose a statistician is asked to design a ...
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33 views

Adjusting for experimentally-caused panel attrition when evaluating treatment effects

This question involves a questionable hypothetical scenario, but please bear with me. Suppose I ran an experiment in a coffee stand where the treatment was playing country music instead of the usual ...
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419 views

Difference-in-difference in panel data

Under which conditions should we expect the difference-in-difference estimate to be equal to the equivalent panel data model? Strictly speaking, whenever we have a experiment that offers a well ...
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3answers
263 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 ...
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1answer
137 views

Weighted Wilcoxon ranksum test

I am using Stata for a survival analysis project involving inverse probability weighting (IPW). The question has arisen as to how to analyze weighted continuous data between two groups with a Wilcoxon ...
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2answers
777 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: ...
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2answers
771 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.
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102 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 ...
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52 views

Roy model question

I am referring to G.S. Maddala: Limited Dependent and Qualitative Variables in Econometrics, pages 257-258. I add the relevant screenshots here: My question is, why is ...
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1answer
208 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 ...
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190 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 ...
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1answer
90 views

Finding the corresponding bayesian network of a predefined joint probability distribution

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?
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1answer
67 views

Are latent variable models modelling causality?

Is the purpose of latent variable models to model causality, where the causes are not observable i.e. latent? Are latent variables modelling causes of the observable variables? Thanks and regards!
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44 views

Terminology to Use

Should you say a factor is associated with a disease or disease risk? For example, which is better to say: Smoking is associated with lung cancer Smoking is associated with lung cancer risk
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734 views

Econometrics: Sargan test

Here are 3 questions about econometrics and R codes. Test the endogeneity of the variable EDUC: ...
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411 views

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? ...
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966 views

What does plausibility or plausibile mechanism mean?

In Bradford Hill criteria for causality Plausibility: A plausible mechanism between cause and effect is helpful (but Hill noted that knowledge of the mechanism is limited by current knowledge). ...
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1answer
157 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 ...
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1answer
95 views

Multiple imputation for variables used to calculate regression weights

My basic question: is there anything that you can't impute using MI? My more complicated question: Consider the regression $Y=\rho T+X'\beta+\epsilon$. For whatever reason, you want to weight the ...
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1answer
170 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 ...
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1answer
106 views

How to quantify mis-specification bias and compare against smoothing bias for a non-parametric estimate of a randomly allocated continuous treatment?

Suppose that there is a data-generating process $$ y = \alpha + g(x) + \epsilon $$ which is to say that an outcome is some function of $x$. Suppose that $x$ is randomly assigned, so ...
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4answers
9k 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 ...
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1answer
81 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 ...
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1answer
29 views

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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83 views

Counterfactuals for Variables with Negative Values

Lets imagine I have estimated the following simple linear regression model: $y_{i} = 10 + 0.5x_{i} + \varepsilon_{i} $, and want to work out the counter-factual, or what would $ y_{i}$ be in the ...
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2answers
769 views

Relation between causal inference and prediction (classification and regression)

I was wondering what relation and differences are between causal inference and prediction (classification and regression)? For example, In prediction, we have predictor/input variables and ...
2
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1answer
80 views

Relative efficiency of matching versus adjustment to handle confounding effects in highly disproportionate populations

I am reviewing a paper where the authors compare cancer outcomes (binary) between two groups, one having a small sample size of 200 and the other having over 55,000. The authors then claim that, due ...
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2answers
243 views

Causality, omitted variable bias

This might be a basic question, but I want to be sure that what I'm doing is right. I have a model that suggests that variable X causes both Y and Z. When I regress Y on X, or Z on X, I get positive ...
3
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1answer
104 views

I have GBs of Event-Based Data. How do I figure out causation?

I have a lot of event-based data about users of our website. For example, data in the format (verb, timestamp). There's about 10 or so different verbs (call them A, B, C, etc). I'm interested in ...
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618 views

Do we need Overlap/Common Support in case of a parametric regression?

If I want to make a causal statement based on selection on observables. One typically assumes "Common Support" (/"Overlap") - which means that for any value of the confounding variables X a unit i can ...
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513 views

An alternative to “Granger Causality” test when (short) time series are not stationary?

I have two short time series (x and y), and I wish to find out if x "effects" (is correlated with) y. Obviously, since the two are time series, using a simple correlation is the wrong way to go. I ...