R2 is not a good effect size measure, but none of these arguments should convince anyone. http://data.library.virginia.edu/is-r-squared-useless/ …
H2 is a variance type metric, actually. You can and in some cases should convert to correlation-type metric.
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Another criterion: whether the metric is comparable across models, datasets, range restriction etc. There's likely no one best metric.
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And whether it is susceptible to outliers etc. E.g. the squared-family metrics are strongly affected, but e.g. median absolute error is not.
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True, doesn't mean it doesn't' suffer from a HUGE interpretation problem (re: everyone that thinks genes don't affect psychological life)
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Many interpret H2 as intrinsic genetic effects whereas it may be mediated by behavior, which could be targeted by intervention.
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And intrinsic genetic effects could still be targets of the interventions if one can find the internal pathways. So yeah. Not easy.
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