17

Strictly speaking, "Granger causality" is not at all about causality. It's about predictive ability / time precedence, you want to check whether one time series is useful to predict another time series---it's suited for claims like "usually A happens before B happens" or "knowing A helps me predict B will happen, but not the other way around" (even after ...


12

If the outcome depends on treatment as well as other observable factors, controlling for the latter often improves the precision of the impact estimate (i.e., the standard error of the treatment effect will be smaller). When sample size is small, this can be helpful. Here's a simple simulation where even though treatment is random, the standard error ...


10

Yes, it makes sense and in this case the coefficient for the interaction of the post-treatment indicator and the treatment variable gives you the effect on the outcome that results from an increase in the treatment intensity. An example of this is the paper by Acemoglu, Autor and Lyle (2004), where they estimate the effect of World War II on female labor ...


10

Race and ethnicity are variables that cannot be "controlled" in experiments, since it is not possible for the researcher to assign or change this characteristic of the study participant.$^\dagger$ For this reason, causal inference relating to race and ethnicity cannot generally rely on randomised controlled trials, and must instead fall back on uncontrolled ...


8

I think you are getting hung up on the difference between potential outcomes $(Y^0,Y^1)$ and the observed outcome $Y$. The latter is very much influenced by treatment, but we hope the former pair is not. Here's the intuition (putting aside conditioning on $X$ for simplicity) about the observed outcome. For each observation, the realized outcome can be ...


8

How would you describe the uncoundedness/ignorability assumption to somebody who has not studied the RCM? Regarding intuition to somebody not versed in causal inference, I think this is where you could use graphs. They are intuitive in the sense that they visually show "flow" and they will also make clear what ignorability substantively means in the real ...


7

Based on the comments and the availability of such a large control group, I would probably advise to do in a step first exact matching on age groups and sex, and perhaps common disease groups. Hereby, you built different strata. In a second step, you can apply propensity score matching to ensure that treatment and control group are as balanced as possible ...


7

The documentation for Matching is sadly fairly incomplete, leaving what it does quite mysterious. What is clear is that it takes a different approach from Stuart (2010) (and the Ho, Imai, King, and Stuart camp) in estimating treatment effects and their standard errors. Rather, it takes heavy inspiration from Abadie & Imbens (2006, 2011), who describe ...


6

From a frequentist perspective, an unadjusted comparison based on the permutation distribution can always be justified following a (properly) randomized study. A similar justification can be made for inference based on common parametric distributions (e.g., the $t$ distribution or $F$ distribution) due to their similarity to the permutation distribution. In ...


6

What is typically done is that you plot the averages of the outcome variables for your treatment and control group over time. So the control group here are naturally all those who did not receive the treatment whilst the treatment group are those who receive any intensity of the treatment. That was done for instance in this presentation (slides 25 and 26, ...


6

Removing good data from an analysis is scientifically suspect in my humble opinion, and naive matching methods are inefficient. It may be very easy to adjust for patient characteristics using ordinary regression models, paying attention to linearity assumptions etc. Of course it is a good idea to look at overlap in covariate distributions across treatment ...


6

Adding baseline as a covariate is statistically acceptable - or in fact advisable - in observational studies, as well as RCTs. It is typically just not sufficient to ensure valid inference, and adjustment/stratification for propensity scores (or some other methods that try to deal with the non-randomized nature of the comparison - e.g. structural equation ...


6

Let me use $X$ for the treatment, $Y$ for the observed outcome and $Y(x)$ for the potential outcome under $X = x$. Consistency means that for an individual $i$, his observed outcome $Y_i$ when $X_i = x$ is his potential outcome $Y_{i}(x)$. Or, more formally: $$X_i = x \implies Y_i(x) = Y_i$$ When the treatment is binary ($X \in \{0,1\}$) consistency ...


5

Let $R_i$ be a dummy which equals one for respondents and zero for non-respondents, $Y_i$ the outcome and $D_i$ the treatment variable from your randomized experiment. You cannot observe the counterfactual quantities that you want to compare, i.e. $E[Y_{i1}|R_i = 0|D_i = 1]$ and $E[Y_{i0}|R_i = 0, D_i = 0]$, due to non-response but you know their probability ...


5

In R you can just pass the vector of effects to the qqnorm function. If you want the points labeled then save the result of qqnorm and use that with the text or identify functions. mydata <- expand.grid( A=c(-1,1), B=c(-1,1), C=c(-1,1), D=c(-1,1) ) mydata$y <- rnorm( nrow(mydata) ) fit <- lm( y ~ .^4, data=mydata ) tmp <- qqnorm( coef(fit) ) ...


5

Let me paraphrase your question: "I statistically tested a hypothesis and obtained some p-values. Can I use these p-values to evaluate a different hypothesis?" I don't think that is a good idea. You are asking two different scientific questions. Consequently, you'll want to use two different tests to evaluate the two different hypotheses. The first question ...


5

@Michelle raises a good question--it depends on what the answer is. However, at first blush, I suspect that you could just multiply your percentages by your N's and get counts for each cell. Then you would have a straightforward 3x2 chi-squared test setup. I get the following: A B Treatment 1 12 18 Treatment 2 11? ...


5

The best bound you can get is due to a variant of the Cauchy-Schwarz inequality: $$|Cov(X,Y)| \leq \sqrt{Var(X) \cdot Var(Y)}$$ This is of course very broad, as the covariance can be negative but the right hand side is always positive. It ensures that the $2 \times 2$-covariance matrix between $X$ and $Y$ is positive semidefinite. I'm afraid that the bonus ...


5

You construct the policy dummy the way you first describe it, i.e. create a column of zeroes. Then for each firm you replace this with ones if a firm is in the treatment group AND it is in the post-treatment period. Something like this $$ \begin{array}{ccccc} \text{firm} & \text{time} & \text{treated} & \text{post} & \text{policy} \\ \hline ...


4

The usual way would be to measure the treatment effect as the difference of both effects: $\beta_{Treated}$ - $\beta_{control}\equiv \theta$. In your case, you need to calculate $\theta$ and then test its significance. The difference in p-values may eventually give you some elements for discussion (or rather speculation ?) but the discussion will become ...


4

This would be the standard propensity score estimator. For a binary treatment the conditional independence assumption (CIA) states that $$ \newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}} \def\independent#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}} T_i\perp\hspace{-0.28cm}\perp (Y_{i0}, Y_{i1})|X_i $$ i.e. the treatment is ...


4

What do marginal and conditional relate to? Assuming the treatment effects are accurately estimated, the conditional treatment effect relates to the estimated effect on an individual whereas the marginal treatment effect relates to the effect on the entire population. When do the estimates differ? It sounds odd that the two estimates can differ, but they ...


4

Provided there is some justification for an exponential decay model, you could try the gnls function from package nlme. This allows you to compare treatments and model variance heterogeneity. Here is something to get you started: library(ggplot2) p <- ggplot(DF, aes(time, value, color = treatment)) + geom_point() Get starting values by fitting separate ...


4

All matching estimators for the treatment on the treated effect can be written in the form $$ \frac{1}{n_T} \sum_{i \in \{d_i=1\}} \left[ y_{1i} - \sum_{j \in \{d_j = 0 \}} w_{ij} \cdot y_{0j} \right] ,$$ where $w_{ij}$ is the weight placed on the $j$th untreated observation as a counterfactual for the $i$th treated observation, and $n_T$ is the number of ...


4

Let's imagine you have a group of $n$ people and you want to separate them between treatment and control groups. Bernoulli trials In a bernoulli assignment, you consider each person individually and "flip" a coin with probability $p$ for assigning the treatment to that person. On average, you will have $np$ persons in the treatment group, but you could ...


4

Let's switch from $r_t$ to the more standard notation $Y_t$, which is the potential outcome corresponding to setting treatment $z$ to $t$. The whole point of propensity score analysis is to estimate a causal quantity, usually $E[Y_1-Y_0]$, using observed data. Not all of the potential outcomes are observed because only the potential outcome corresponding to ...


4

There are two main strategies which have been suggested in the literature. One possibility is to use some form of imputation. There are two R packages available from CRAN which take different approaches. SAMURAI assumes you have some information from the article about whether the authors saw their results as very positive, positive, and so on but did not ...


3

You investigate a paired data situation, as you mentioned, however, you treated it like independent. You should run the bootstrap on differences of pre/post measurements of each patient. Then, see, whether the interval contains zero. Although it's not generally advisable, in the situation as you describe it applying the one-tailed spcification is reasonable. ...


3

This has been asked on the Statalist too. The post here mentions the user-written command doseresponse (a multivalued treatment effect evaluation method to assess the effect of a drug that participants could take in different levels of intensity) or the subroutine gpscore. The relevant reference is Bia, M. and Mattei, A. (2008) "A STATA Package for the ...


3

In the Blinder Oaxaca decomposition, which is an econometric technique normally used to compare logged income, the interest is not just in the difference in the means, but also whether the difference is more due to: returns on human capital (so the coefficient values differ between the male and female equations), or human capital levels and other person-...


Only top voted, non community-wiki answers of a minimum length are eligible