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The pull to 0 is one standard approach to fixed effects, specifically the within-estimator formulation where each variable has its individual-specific mean subtracted from it. I like the within-estimator version of FE for the graph because it's a clear application of "remove all between-Individual differences" that doesn't require any further explanation.
Adding seeds, and switching the descriptive HTML (currently at nickchk.com/causalgraphs.html) to markdown are good ideas, I'll add them to my to-do.
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Thanks Nick for explaining the within-estimator. I understand your point about the within-estimator. More generally in applied statistics, people use dummy variables for categorical variables, we call that "fixed-effects", while we name random effects for those variables that are generated from another distribution and have their hyper-parameters, but that appears to be different from what you mean here.
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The within-estimator is equivalent to the version using dummy variables (at least in terms of the coefficients on the regressors in the model), it's just a different way of calculating the estimator. You're right that the intuition for the within-estimator doesn't generalize so well to random effects, which is a downside.
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