Here is how one version of matching workspic.twitter.com/HGYRSgG2KC
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I've been getting used to gganimate and thought it would be useful to put together some illustrations of what various causal inference methods *actually do to data* and how they work. Here, for example, is what it means to control for a (binary) variablepic.twitter.com/lmEvJSPQgY
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Instrumental variables (the Wald estimator, to be specific)pic.twitter.com/DNaVftuXfp
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Fixed effects (really just the animation for controlling again, but with more categories)pic.twitter.com/O7O16U0Fjj
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This is for a class I'm designing on programming and causal inference (h/t
@causalinf) designed to go BEFORE the rest of the econometrics sequence. The idea is teaching concepts before methods. Notice that none of these graphs use regression! It's not necessary!Show this thread -
Here's a link to a page with these graphs alongside DAGs and more explanatory detail, if you want something to link your students to. Also if you have any ideas for other methods I should animate let me know. http://nickchk.com/causalgraphs.html …
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Update for anyone still looking at this version of the thread. New version of the thread is up, with slower graphs:https://twitter.com/nickchk/status/1068215492458905600 …
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When controlling for a continuous variable v, one would fit a linear with OLS (i.e. a normal distribution as error distribution model) as a function of v, and then normalize the predicted means by subtracting them for each value of v? Or would one rather discretize v?
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You'd fit a linear with OLS and subtract the predicted values (no need to normalize). Formally this is known as the Frisch-Waugh-Lovell theorem (which also generalizes to multiple controls) if you want to see more about the process
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Excuse my sloppiness; by normalization I was referring to zero-centering the means. However, wouldn't it also conceivable that v not only affects the mean, but also the dispersion? So one would fit and normalize the variances too. Is that commonly done?
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A correlation between a control variable and the variance of the error term is known as heteroskedasticity, and can be addressed in a few different ways, one of which is robust standard errors, which doesn't normalize variances exactly but you could make an analogy to that
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Exactly what I was looking for! Coming from a ML angle, the problem of transforming pdfs for different settings of the control variable to the same pdf reminded me of (optimal) transport theory. It seems one should be able ot use CycleGAN to map all pdfs to one without data loss.
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I mean sufficiently little data loss such that it is possible to map the data back based on the control variable.
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I think that would be possible as long as you held onto the predictive model used to adjust. You'd just adjust back.
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Yes. CycleGAN is defined by a cycle consistency loss which enforces a bijection between multiple domains (in this case between different settings of the control var). Which points are mapped to one another seems ill-defined though, so not sure it would work well.
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Phenomenal teaching tool! Would love to show these to students if ok. Thanks :)
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Oh absolutely! That's what it's for
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Can I please use the r code for teaching? I am developing an R visualization course for the summer term.
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Absolutely! Go for it
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