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They say that they account for the log of the family income, but do not elaborate on that point beyond saying they do (at least after a quick skim). It seems to me that this would be extremely difficult - does anyone have insight on how they might have done this?

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Probably a fixed multiplier. There's a tremendous amount missing from this study, and I wouldn't take any of its conclusions at face value.

Usually, you do a multivariate statistical analysis, and "accounting for" means, it was one of the variables thrown in.

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