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First of all, I don't think this should be treated as a strict dichotomy: "predictive models can never establish causal inference." There are various situations in which a predictive model gives us "pretty darn good" confidence that a given causal relationship exists. So what I'd say is that predictive models - no matter how sophisticated ...


10

I think this explanation is best approached sequentially. Start with a simple story: When my dog Winston wags his tail, that indicates he is happy. For instance, he never wags it at the vet, wags it a bit when I get his leash, and wags a whole lot when I also grab a tennis ball. But if I wag Winston's tail for him, it usually has the opposite effect. In ...


9

I don't think you even need to posit a covariate adjustment set $\textbf{Z}$ nor the indexation of black-box models to convey in layman terms the main point. Assume the following: $y$ is number of people drowning in a given month in a given city $x$ is number of ice-cream sold in a given month in a given city $u$ is temperature in a given month in a given ...


6

It's really important to distinguish the observed outome, $Y_i$, and the potential outcomes, $(Y_i(1), Y_i(0))$. The observed outcomes are, well, simply the outcome you observed for each subject. The potential outcomes are the outcomes that you would observe if a patient was given a certain treatment. If you have two versions of a treatment (say $0$ and $1$ ...


6

But is $Y = aX + cZ + e$ (as a regression model, not a math equation) also a causal model (albeit a "wrong" causal model)? If I manipulate $X$ it tells me what happens to $Y$. Doesn't it correspond to the causal graph $X \rightarrow Y, Z \rightarrow Y$ ? It may correspond to the causal graph $X \rightarrow Y, Z \rightarrow Y$... ... But it can ...


5

tl;dr: A book reviewer with the initials F.A.D in a 1900 issue of Nature appears to be the first to publish the phrase "correlation does not imply causation." Long form answer Depending on whether you are looking for the exact words "correlation does not imply causation" (note also "correlation is not causation"), or just want ...


4

Correlation does not equal causation. Predictive models using advanced techniques such as machine learning can be quite good at finding associations between predictive variables and an outcome, but this isn't the same as determining the causal relationships between those variables. For example, as a researcher you may find a strong correlation between ...


3

SUTVA says that $\delta_i(d)$ doesn't depend on treatment assignment for individuals other than $i$. Ignorability says it doesn't depend on treatment assignment for individual $i$.


2

Oo Oo! I'm a mathematical layperson! Let's see if I can do this: TLDR: I use predictions (or "predictive models") to prepare for events beyond my control without having to know what actually causes them. I might posit that a lay predictive model is "whether the weather report says it will rain this weekend". I may not care what will ...


2

The ATE is an estimand involving unseen potential outcomes and is defined at $E[Y^1-Y^0]$, where $Y^1$ and $Y^0$ are the potential outcomes under treatment and control. Under the main causal assumptions, the ATE is equal to $E[E[Y|A = 1, V]-E[Y|A=0, V]]$, where $V$ is a valid adjustment set. Let's call $E[E[Y|A = 1, V]-E[Y|A=0, V]]$ the average marginal ...


2

That must be one heavy cat! Clearly he must be responsible for crushing the awning. I found this one on LinkedIn. Just because you saw some things does not mean that one caused the other. We are free to assume and to entertain different hypotheses, but correlation does not imply causation.


2

When conducting these kinds of experiments there is a natural control-group for each marginal and conditional effect in the experiment. The figure below shows an experimental flowchart for the possible categories of each participant. The "No Treat" category acts as the control group for determining the marginal effects of Treatment A or B, the &...


2

What's the purpose of do-calculus? The do-calculus is an axiomatic system for replacing probability formulas containing the do operator with ordinary conditional probabilities. Criterions like backdoor and frontdoor can be considered as consequence of do-calculus. Them are verifiable under some conditions. However, as suggested by Adrian Keister, those ...


2

The question is essentially asking you to imagine running a regression of $X$ on $Y$ and then plugging in the value of $Y$ to get the predicted value of $X$. We known that $\beta_{YX}$, the coefficient on $X$ in $f_Y$, is equal to $\frac{\text{Cov}(Y, X)}{\text{Var}(X)}$. Our goal is to compute $\beta_{XY}$, the coefficient on $Y$ in a hypothetical ...


1

In (a), $X$ and $Y$ are unconditionally d-separated because of the unconditioned-upon collider $Z_1$, which blocks all paths from $X$ to $Y$. conditioning on $Z_2$ does not change this fact, and so $X$ and $Y$ remain d-separated after conditioning on $Z_2$.


1

In causal inference you can think about identifiability as the condition that permit to measure causal quantity from observed data. Among parametric models is the condition that permit to estimate causal parameters from regressional. Formally $E[Y|do(X)] = E[Y|X] $ Can be consider as identifiability condition. Identifiability condition is one key point of ...


1

From the plot you provide I do not see a significant trend of body weight over time. You can try to fit a regression to see if the coefficient of time is significant statistically (p value) or practically (effect size compared to outcome scale). My guess is it won't be, so you can just proceed to calculate average treatment effect. If your no-treatment group ...


1

I would say this is a matter of terminology. What people in causality mean when they talk about mechanisms (also known as Independent Causal Mechanisms, causal Markov kernels, causal conditionals, etc.) are the "true" causal conditional distributions. In your case, you have only one mechanism $P(B \mid A)$. As you correctly pointed out, the ...


1

continuous variables cannot be used as confounders directly in a regression model without some esoteric encoding This is false. You can include age into your model as is. If you believe the effect of age on risk is nonlinear, you can use an appropriate transformation of age instead. (Encoding is needed for categorical variables, not continuous ones, and is ...


1

OP mentioned that they ended up selecting control groups for the treatments independently. In this case, if there is no clear bias in the assignment mechanisms of treatment A and treatment B (e.g. somehow applying treatment B also increases probability of treatment A), the subtraction in the calculation of average treatment effect should naturally cancel out ...


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