andrew_gelman_stats andrew_gelman_stats-2014 andrew_gelman_stats-2014-2204 knowledge-graph by maker-knowledge-mining
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Introduction: XL sent me this paper , “A Fruitful Resolution to Simpson’s Paradox via Multi-Resolution Inference.” I told Keli and Xiao-Li that I wasn’t sure I fully understood the paper—as usual, XL is subtle and sophisticated, also I only get about half of his jokes—but I sent along these thoughts: 1. I do not think counterfactuals or potential outcomes are necessary for Simpson’s paradox. I say this because one can set up Simpson’s paradox with variables that cannot be manipulated, or for which manipulations are not directly of interest. 2. Simpson’s paradox is part of a more general issue that regression coefs change if you add more predictors, the flipping of sign is not really necessary. Here’s an example that I use in my teaching that illustrates both points: I can run a regression predicting income from sex and height. I find that the coef of sex is $10,000 (i.e., comparing a man and woman of the same height, on average the man will make $10,000 more) and the coefficient of h
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1 Simpson’s paradox is part of a more general issue that regression coefs change if you add more predictors, the flipping of sign is not really necessary. [sent-6, score-0.285]
2 , comparing a man and woman of the same height, on average the man will make $10,000 more) and the coefficient of height is $500 (i. [sent-10, score-0.887]
3 But the coef of sex in the above model seems very difficult to interpret: why compare a man and a woman who are both 66 inches tall, for example? [sent-15, score-0.682]
4 Keli replied: There are variables which cannot be manipulated by a human, but it is still possible to imagine hypothetical manipulations. [sent-18, score-0.399]
5 For example, we discuss how the color of a certain species of a plant is not really manipulable (it comes with the species). [sent-19, score-0.298]
6 But one can imagine some sort of “proto”-plant which is that plant before it had color attached. [sent-20, score-0.347]
7 We can now talk about manipulation of color for the proto-plant. [sent-21, score-0.423]
8 The key however is that our unit of analysis has changed: when we think about manipulation of color, our fundamental unit is no longer plant but rather proto-plant. [sent-22, score-0.867]
9 So we can always imagine hypothetical manipulations, but we need to keep careful accounting of what our unit of analysis is. [sent-23, score-0.514]
10 Now to the second part of the question: why should we be interested in these hypothetical manipulations in the first place if we cannot perform the actual manipulation? [sent-24, score-0.32]
11 Now suppose we want to study the effect of height on income. [sent-27, score-0.472]
12 Our point is that to answer this question, you need to think about manipulation of height, even if it is only a hypothetical manipulation. [sent-29, score-0.561]
13 In particular, when we think about the hypothetical manipulation of height, our unit of analysis is no longer an individual from the dataset (since these individuals come with height already). [sent-30, score-1.32]
14 These “proto”-individuals have attributes but height is not one of these attributes—hence why we can think about manipulation of height. [sent-32, score-0.98]
15 We should include in the regression all predictors which are attributes of this “proto”-individual, but leave out predictors which are not attributes of this “proto”-individual. [sent-33, score-0.681]
16 When you say “indeed it would seem somehow ‘wrong’ to regress on height _without_ controlling for sex”, what you are implicitly doing in your mind is conceiving of this “proto”-individual and realizing that sex is in fact an attribute of this “proto”-individual. [sent-34, score-0.927]
17 Similarly, when you say, “why compare a man and a woman who are both 66 inches tall, for example? [sent-35, score-0.346]
18 ” what you have done is to imagine a hypothetical manipulation of gender. [sent-36, score-0.63]
19 Hence we should not include height in the regression if our goal is to learn about the effect of gender. [sent-38, score-0.621]
20 And I also think I can interpret those regressions without having to think about manipulation of height or of sex—to me, these are between-person comparisons, not requiring within-person manipulations. [sent-40, score-0.981]
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