# 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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### The difference between average and marginal treatment effect

I have been reading some papers, and I am unclear about the specific definitions of Average Treatment Effect (ATE), and Marginal Treatment Effect (MTE). Are they the same? According to Austin... ...
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### Selecting Control Time Series for CausalImpact package in R

I'm currently using the CausalImpact package in R to analyze advertising impact on single store sales. I am working with daily sales data from nearly 2,000 locations. Of the 2,000 stores, only about ...
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### Causal impact response time series

I am trying to analyze the effects of an online advertising campaign. The campaign was in market globally except for "Country A". In my response time series, I am using orders from all countries ...
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### Statistical analysis using small sample size N=11 or 15

I am analyzing firm level data to unpack the cost of producing a renewable energy technology. I have dependent variable as the production cost of the technology, independent variables are three ...
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### Unconfoundedness in Rubin's Causal Model- Layman's explanation

When implementing Rubin's causal model, one of the (untestable) assumptions that we need is unconfoundedness, which means $$(Y(0),Y(1))\perp T|X$$ Where the LHS are the counterfactuals, the T is the ...
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### How to distinguish a causal chain model from a double effect model?

I am used a linear mixed model on two datasets (two different species), with the same explanatory variable (an environmental variable) for fixed effects. I then select the top 0.1% response ...
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### Exogeneity Interpretation

Consider the following linear regression model:$$Y=X'\beta+u$$ If I wish to estimate this equation by OLS, I have to first think of ways in which the estimator might be biased. More speciifcally, I ...
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### Why do I still need to include control after propensity score matching?

On page 209 of Gelman and Hill book, the authors suggest that Having created and checked appropriateness of the matches by examining balance, we fit a regression model just on the matched data ...
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### CausalImpact Vs Synth

Can CausalImpact package be used in lieu of the Synth package to create a synthetic control ? The R implementation of the Synth package is very confusing compared to the Stata demo for the Synth ...
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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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### CausalImpact with Panel Data

The way I understand it, the CausalImpact package estimates a Bayesian model meant to analyse time-series data. What if, instead, I want to use panel data (i.e. repeated observations of the same ...
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### Estimate a curvilinear relationship (inverted U shaped) using difference-in-differences estimator

If I want to estimate a potential curvilinear relationship (inverted U shaped) between X and Y, whether it is possible to use difference-in-differences regression (suppose I can explore variations in ...
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### Fixed effects in regression discontinuity design

I want to do a non parametric RDD type analysis to know the impact of an intervention (a single dummy variable) on an outcome variable. I have several 'boundaries' (which are actually different ...
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### How do I estimate sensitivity of two outcomes variables from a difference-in-differences setup?

Say I estimate the following multi-period DID equations separately: $\frac{Y^1_{it}}{A_{it}} = \alpha^1_i + \alpha^1_t + \tau^1 D_i\times Post + \beta^1C_{it} + \epsilon^1_{it}$ ...
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### Prior on effect of treatment using CausalImpact library in R

I'm using the package causalImpact in R to estimate the causal effect of an intervention in a time series. However, I have strong prior information that the effect can't be negative. How can I encode ...
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### decomposing average treatment effect

Suppose I estimate a difference-in-difference (DID) model on some outcome variable Y, and say I found a statistically significant average treatment effect (ATE). Using the same DID model on another ...
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### Durbin-Watson: test exogeneity

I have a time series for which I have built a linear regression, say $Y(t)=\beta X(t)$. A regression implies that $Y$ is actually a function of $X$ (that is, $Y(X)$), but not the other way around ...
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### Experimental treatments assigned via email how best estimate average treatment effects?

A growing number of social experiments are conducted outside of the laboratory, and by assigning the treatment condition through emails (e.g., often the content of the email is the intervention ...
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### Methods of Treatment Effect Heterogeneity Estimation (Observation Data)

Given observational data, where a "treatment" is chosen by the unit of observation or not, are there any standard methods of ascertaining not just if the treatment has effect overall (ATT), but ...
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### Understanding the direction & strength of a correlation, & causal status, from a chi-squared test

I am analyzing Stack Overflow Posts. So I have a database with 1000000 questions, their current score (upvote or downvote) and a flag, that there is a source code part in the question (or not). So I ...
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### Robust Coefficients For Differences in Differences

I have a panel data set which I am looking to analyze for relationships/causality using the OLS differences-in-differences method. The panel data includes multiple observations over time for various ...
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### Causal Trees to Estimate Heterogenous Treatment Effects: Transformed Outcomes [Machine Learning in Python]

I am interested in using off-the-shelf tools like scikit-learn for Python to implement the Athey-Imbens recommendation for estimating treatment effect ...
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### fixed effects question

I am analyzing survey respondent data. Respondents are nested within regions and are surveyed 4 times. Over the 4 time periods, different regions undergo a policy change (go from 0 to 1) randomly (or ...
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### why are these uplift estimates different?

I recently stumbled upon an ODSC presentation: Machine Learning Based Personalization Using Uplift Analytics: Examples and Applications Uplift wherein two methods for "uplift" estimation are provided: ...
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### CausalImpact - Should I use more than one control?

In the intro document (https://google.github.io/CausalImpact/CausalImpact.html) it suggests that using one predictor is not ideal. Am I current in understand that they mean one control? If so, should ...
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### Challenging Propensity Score/Causal Inference Problem

I am reaching out to the Cross-Validated statistical community seeking suggestions on a challenging problem on which I'm working. I've been asked to look into a problem related to electronic ...
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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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### How to incorporate characteristics of the object of outcome variables as predictors in model

I'm working with survey data for a social science research topic. The particulars aren't super important, so I'll use a simplified version to make it easier to understand what I'm trying to do. I say ...
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### Using spike-slab to fit log-link GLM Gamma

I am attempting to model the causal impact (using CausalImpact package in R) of a know discrete event on the change in medical expenditures. I have 12 pre and 6 post period observations and upwards of ...
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### Variables with low coefficients/high p-values in multiple linear regression highly correlated to significant predictors

This is possibly a very naive question: I am watching Hastie and Tibshiranie's class ("Introduction to Statistical Learning"), and at the end of this lecture, Tibshirani gives example of a multiple ...
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### CausalImpact - Is pre-processing of covariates required?

I'm using the CausalImpact to evaluate the effect of a programme. My covariates are seasonal and I wonder whether I need to deseasonalise/ detrend the regressors before using the R package? Hal ...
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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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### CausalImpact on single time series

Today I have tried to play a little with CausalImpact R-package https://google.github.io/CausalImpact/CausalImpact.html (Brodersen et al. 2015) to explore the impact of some decissions in a sales data ...
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### How can I analyze / compare point-of-sales data between stores with different product offerings?

Let's say I have two stores, A and B, and let's say I have two products in the same department: product 1 and product 2. Let store B have product 2 which store A doesn't have, both stores have product ...
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### Modeling complex mechanism with regression (or similar method)

There are six variables A, A', B, C, D, and D' and they are related as shown in the figure below. I want to know the effect of A on C through B. I firstly thought to use 2SLS, but since A and C are ...
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### Questions about the paper “Inferring causal impact using Bayesian structural time series models”

I am simulating this model in the paper Brodersen et al. (2015) and found I have difficulties on figuring out how to choose the starting point of Bayesian inference. To be explicit, to my ...
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### How to test whether it is valid causal inference

definition of average causal effect $$ACE = E(C_1) - E(C_0)$$ $$ACE = E(Y|X=1) - E(Y|X=0)$$ given the condition that $$X \bot (Y(0), Y(1))$$ So if I have a regression ...
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### Regression discontinuity design with multiple cutoffs

When we have an RD with multiple cutoffs, and we pool all observations and estimate the treatment effect across cutoffs, what does the pooled estimate identify? I have found one paper using a RDD ...
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### What is the best way to visualize difference-in-differences (multi-period) regression?

What's the best way to visualize difference-in-differences for both binary and continuous treatment? Do I regress the outcome variable on the set of controls but exclude the treatment variable and ...
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### How do I interpret a “difference-in-differences” model with continuous treatment?

How do I interpret the ATE coefficient (i.e., the post-treatment indicator interacted with the continuous variable)? Does it make sense? Should I break it down into subgroups and just run a fixed ...
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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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### How to show influence of a treatment group?

Instrumental variables regression is often used in economics to infer causal relationships. For instance, if we are interested in the effect of remittances (X) from abroad on home consumption (Y), we ...
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### How can I compute cross-correlation and auto-correlation in R using pooled data?

I'm trying to perform a lagged linear regression on time series data sourced from ~10,000 hospital patients, for the purpose of estimating causal relationships between administration of a drug and a ...
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### Causal inference from Cross sectional study

As far I know that, causal inference can make for longitudinal study. Is their anyway way to make causal inference from cross sectional study design? If yes, how can I do this? Please share if any ...
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### Dealing with constraints in probabilistic graphical models

Suppose I have a graphical model with i.i.d. $\Lambda_i \sim exp(\lambda),\ \ i = 1,...,n$, and $\bf{\Lambda} = \sum_{i=1}^{n}\Lambda_i$. Imagine that that these $n$ lambda and this capital ...
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### How to identify the underlying mechnism in regression (to preserve the causality)?

everyone,I recently encounter a problem when doing some empirical work. Say, with a cross section dataset,I'm studying the effect from A to Y, including a branch of control variables X,of which A is a ...
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### How to do regression if one is not sure of dependent variable?

I have data on age, gender, height and weight of subjects, and also levels of 2 chemicals in blood of these subjects (chem1 and chem2). It is not clear whether chem1 affects chem2 or chem2 affects ...
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### Isolating influence of sampling from actual change

Say I want to evaluate teams' batting coaches in a hypothetical baseball league. It's an unusual league in that there is no control over (and large fluctuation within) the number of at-bats each ...