I'm sorry to be publicly ragging on your analysis but it really doesn't show what you want it to show :/
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Replying to @eigenrobot
No no, rag away. That's what it's there for. Again, I'm not blind to the endogeneity in my kitchen sink model, so just consider the 0 order analysis. The correlation is respectable, but not predominant.
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so--it's pretty tricky trying to isolate the effect of whatever AFQT proxies for, unless you have a strong theoretical model you might SORT of take it as exogenous given the heritability of IQ (that increases with age!) but pretty plausibly lots of childhood effects . . .
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Replying to @eigenrobot @NickWolfinger
might spring into play eg, your parents are probably high IQ if you are, they are plausibly more likely to be able to provide more opportunities for your childhood environment, etc all of this as a preface to saying: you could (with this data set) come up with . . .
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Replying to @eigenrobot @NickWolfinger
a sort-of upper bound on AFQT explanatory power for future earnings by (say) looking at age 18 AFQT (did they give it at 18? at whatever year) and and doing a univariate(ish) nonparametric estimation of (income at 40 | AFQT at 18) say, throw these into a RF and pull the R^2
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Replying to @eigenrobot @NickWolfinger
but, looking at changes in R^2 for all of these explanatory variables with and without AFQT isn't going to get you what you suggested in your analysis, because those other explanatory variables are collectively almost surely quite correlated with AFQT
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Replying to @eigenrobot @NickWolfinger
that is to say, your R^2 = 0.48 probably includes a substantial effect from AFQT (or whatever that proxies) simply mediated by those other, plausibly-downstream variables so getting only a 0.02 R^2 increase from adding it doesn't mean its explanatory power is so limited
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Replying to @eigenrobot @NickWolfinger
the other issue is that unless you're being extremely aggressive about model specification and didn't mention it, your RE panel is not going to pick up the full plausible explanatory power of your variables in the way that a more flexible model class would
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Replying to @eigenrobot
The graph I presented was based on lowess, so was willing to entertain (& model, if necessary) any nonlinear effects. But obviously I didn't see any. Or by model specs do you mean an more exotic estimator than RE?
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yeah something more exotic than RE you could probably do something like RE with a bazillion interactions and some elastic net regularization for a first pass if you want to handle some of these issues
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