I’m not sure what you mean by selective power. I suppose the natural question is “how many extra (e.g.) IQ points do I get for an extra standard deviation of a PGS?” In other words, you want the regression coefficient, where the dependent variable is on some meaningful scale. I stand by my comment, unless you can show a PGS where a 1 s.d. change currently does something big.
The R value is equivalent to the standardized version of the regression coefficient (modulo some statistical details that don’t make a difference here). Therefore it will be linearly related to the regression coefficient, in whichever scale you choose. Meanwhile, the R2 will be nonlinearly related to the regression coefficient, due to being a nonlinear function of R. See also Marco Del Giudice’s paper on the same topic: Are we comparing apples or apples squared? The proportion of explained variance exaggerates differences between effects
Sure. But the most interesting dependent variable isn’t usually “how many standard deviations of Y will I gain”, it’s e.g. “how many years of education will I gain”. In any case, on either scale, is there a PGS where a 1 s.d. change does something big? You might say the most recent EA is a candidate. In one dataset a 1 s.d. increase causes (i.e. within-siblings) about a 4.5 percentage point increase in the probability of university attendance.
I agree that SD units are strictly speaking meaningless and something like this is reelvant. However I’m just saying that R2 does not help over R with this, and in fact makes it worse because R2 is nonlinearly related to the meaningful quantities while R is linearly related to the meaningful quantities.
I do not know how EA PGS relates to meaningful quantities, and to be honest I would not recommend selecting for EA PGS because (to paraphrase one of gwern’s articles) EA measures an input rather than an output (unlike intelligence PGS), and so it is more likely to contain bad stuff too. (IIRC EA PGS contributes to a bunch of mental illnesses, whereas intelligence PGS only contributes to autism and anorexia. And realistically GD too but I haven’t seen explicit data on it yet.)
The R value is equivalent to the standardized version of the regression coefficient (modulo some statistical details that don’t make a difference here). Therefore it will be linearly related to the regression coefficient, in whichever scale you choose. Meanwhile, the R2 will be nonlinearly related to the regression coefficient, due to being a nonlinear function of R. See also Marco Del Giudice’s paper on the same topic: Are we comparing apples or apples squared? The proportion of explained variance exaggerates differences between effects
Sure. But the most interesting dependent variable isn’t usually “how many standard deviations of Y will I gain”, it’s e.g. “how many years of education will I gain”. In any case, on either scale, is there a PGS where a 1 s.d. change does something big? You might say the most recent EA is a candidate. In one dataset a 1 s.d. increase causes (i.e. within-siblings) about a 4.5 percentage point increase in the probability of university attendance.
I agree that SD units are strictly speaking meaningless and something like this is reelvant. However I’m just saying that R2 does not help over R with this, and in fact makes it worse because R2 is nonlinearly related to the meaningful quantities while R is linearly related to the meaningful quantities.
I do not know how EA PGS relates to meaningful quantities, and to be honest I would not recommend selecting for EA PGS because (to paraphrase one of gwern’s articles) EA measures an input rather than an output (unlike intelligence PGS), and so it is more likely to contain bad stuff too. (IIRC EA PGS contributes to a bunch of mental illnesses, whereas intelligence PGS only contributes to autism and anorexia. And realistically GD too but I haven’t seen explicit data on it yet.)