The explanation by owencb is what I was trying to address. To be explicit about when the offset is being added, I'm suggesting replacing your log1p(x) ≣ log(1 + x) transformation with log(c + x) for c=10 or c=100.
If the choice of log-dollars is just for presentation, it doesn't matter too much. But in a lesswrong-ish context, log-dollars also have connotations of things like the Kelly criterion, where it is taken completely seriously that there's more of a difference between $0 and $1 than between $1 and $3^^^3.
To be explicit about when the offset is being added, I'm suggesting replacing your log1p(x) ≣ log(1 + x) transformation with log(c + x) for c=10 or c=100.
Which will do what, exactly? What does this accomplish? If you think it does something, please explain more clearly, preferably with references explaining why +10 or +100 would make any difference, or even better, make use of the full data which I have provided you and the analysis code, which I also provided you, exactly so criticisms could go beyond vague speculation and produce something firmer.
(If ...
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