[ODP] Crime, income and employment among immigrant groups in Norway and Finland
"Specificity" is preferable to "specificness". Also, the predictive value of variables differs between studies quite a bit, and it would be nice to address that. I am incompetent to address the statistical techniques used in this paper.
P1 = predictor 1, P2 = predictor 2, etc.
V1 = outcome var 1, V2 = outcome var 2, etc.

I understand the labels, but I quoted this sentence "An interaction would be that a given predictor P1 is better at predicting variable V1 than P2, but that P2 is better at predicting V2 than P1" for another reason; it's that I don't understand the meaning of it. By saying V1 and then V2, you have in mind two different regression models.

Originally, the question was asked by Dalliard :

3) "Are some predictors just generally better at predicting than others, or is there an interaction effect between predictor and variables?"

Not sure what you mean by interaction here. The question is whether any of the predictors have unique predictive power.

What you said is whether or not the inclusion of interaction terms will affect the (independent) relative strength of your independent variables, within the same regression. But not two different ones.

Another thing I don't understand, it's because an interaction between predictors is aimed to answer the question about if adding interaction such as P1*P2, with or without squaring them (P1+P2+P2^2+P2^3+P1*P2+P1*P2^2+P1*P2^3), can change your independent coefficients. If the slopes are not linear but curvilinear, the addition of an interaction term will fit the data better. In general, what happens when an interaction is meaningful, is that the main effects (i.e., P1 and P2) will be attenuated. Even if one of the two predictors is more attenuated than the other, I don't think it's relevant here. The interpretation of the main effects becomes totally different when you add interactions. With an interaction, P1 and P2 are the effects net of the interaction, but the interaction itself includes and confounds the effect of both.

I remember several months ago when I attempted to perform regression with wordsum (dep) and race + SES (indep) variables. With the interaction of race*SES, the coefficient of race was near zero. A plot of the predicted values from the model revealed that at the very low SES levels, the BW gap in Wordsum was just meaningless, but that it increases considerably when SES increases. In such a situation, how can we say that race has become less important ?

You cannot say that SES is more important than race just because the interaction term nullifies the main effect of race, because the interaction term confounds the two effects. (when I say "more important", I am of course talking about the direct effects of the independent variables)
"Are some predictors just generally better at predicting than others, or is there an interaction effect between predictor and variables? An example of an interaction effect would be that Islam is better than IQ as predicting crime, while IQ is better at predicting educational attainment."

Interaction in regression analysis means that the predictor variables interact non-additively. For example, if the relation between predictor A and outcome variable Y varies at different levels of predictor B, then there's A x B interaction. Interaction means that aside from the additive main effects of the predictors there are interactive effects between them. To say that there is an interaction between predictor and outcome variables is a misuse of terminology.

You should include also predictor intercorrelations in Table 2 (below the diagonal) because reporting just the correlations between the "prediction vectors" is confusing.
Predictor intercorrelations can be seen in the supplementary material. E.g. here: https://osf.io/3752j/ Rownames are missing due to the way the export function works. They are in the same order as the colnames. So e.g. IQ x Altinok is .91. The 4 non-Islam predictors have high intercorrelations and so are not much use together in MR. Islam does not correlate highly, so it can be combined with one of them in MR.

I will work on a version that fixes the confusion with nonstandard use of "interaction".

So add the predictor correlations to the paper. They are essential for interpreting the results.
Thanks for the clarification, Emil. In fact, it wasn't just the word "interaction" but also the words "predictor" and "outcome" that had confused me. Generally, people refer to regression when they use these terms. If you had used the word interaction alone, I would not have thought about regressions.

I'm unsure about what terminology would fit best.
You know I have already approved, but I just wanted to say that I think the description below is clear.

Are some predictors just generally better at predicting than others, or is there specificity such that while predictor A may be better at predicting outcome X, predictor B is better at predicting outcome Y? An example of this would be that Islam is better than IQ as predicting crime, while IQ is better at predicting educational attainment.
Trust me, if there was really something definitely wrong, I will say it. As you already know, my only problem is with your application of imputation (only three, and no mention of the % of missing cases per variables, and finally, the sentence that seems to suggest that imputation can deal with the problem of "not missing at random", which thing is probably not true in most cases). But since the imputation provides very similar result to the other methods, I don't think I can reject it.

Concerning the last reviewer, maybe try Kevin Beaver. He has published (for instance, see here) on the topic of criminality between racial groups such as blacks and whites.
Dalliard is a harsh critic, so I want to get his approval. I tried to get both Wicherts and Flynn to review the paper, but both declined (Wicherts not enough time citing his presence on other editorial boards, Flynn claimed lack of expertise). The journal ought to have at least some reviewers hostile to genetic models of group differences, but who to invite?

You're not really testing a genetic model here -- so that shouldn't matter in this instance. To begin to test one, this way, you would need to decompose associations by migrant generations.
You know as well as I do, that people who are against the genetic model tend to be against.. everything else too.

Most data isn't broken down by generation. 3rd generations are beginning to emerge in DK. The statistics agency follows them closely to see if they perform better than 2nd gen.

I'll open a separate thread to discuss the matter; the review section of your paper really isn't the place to do so. Can you try to secure approval for this paper?
1) "Islam correlates around weak to moderately with the others (-.14 to -.43, mean -.29)."

--> "correlates weakly to moderately"

2) "that Islam is better than IQ as predicting crime,"

--> "the prevalence of Islam predicts crime better than (national) IQ"

Other than that, the paper is OK and I approve it for publication.