I also have a few rather minor objections: 1) the dig at philosophers near the end is accurate but unnecessary and should be removed; 2) "HM" is close to "Herrnstein & Murray" and could lead to some confusion; 3) the review of what phenomena are Jensen effects could be more thorough. This is a very good paper, however.

Indeed, the black-white income gap is often reversed after such equating (Johnson & Neal, 1998; Nyborg & Jensen, 2001; Heckman et al., 2006), which may signal the presence of discrimination in favor of blacks.

Phillips et al. (1998) found that even after controlling for more than 30 variables related the economic, educational, cognitive, emotional, and health characteristics of parents and grandparents, about a third of the IQ gap in children remained unexplained.

However, there is little evidence of their being overrepresented in relation to the black share of the perpetrators of crime

Specifically, the g loadings and heritability coefficients of tests have been found to be intercorrelated very highly, at close to 1.00 (Rushton & Jensen, 2010).

The principally genetic nature of g has also been confirmed in multivariate behavior genetic analyses where genetic influences on different cognitive abilities have been found to be largely common rather than ability-specific (Plomin & Spinath, 2004; Trzaskowski et al., 2013b).

Kaplan uses Levene’s test for the equality of variances to investigate whether his simulated X-factors inflate IQ variances to a statistically significant extent.

The predominant view among psychometricians and the one that is adopted in this article is that individual differences in intelligence can be conceptualized in terms of a factor hierarchy with a third-level general factor (g), second-level broad ability factors, and first-level test-specific variation (Deary, 2012). Higher-level sources of variation exert a causal influence on the lower levels of the hierarchy.

As it happens, the variances of IQ scores in blacks are typically smaller than those of whites. Jensen (1998, p. 353) found that black standard deviations are usually in the range of 11–14 IQ points, with a mean of 12, compared to the white standard deviation of 15 points.

Accordingly, when Rowe & Cleveland (1996) fitted a biometric structural equation model to math and verbal test data from a genetically informative sample of black and white children, between 36 and 74 percent of the racial test score gaps was accounted for by genetic differences in the best-fitting model.21

it has consistently been found that environmental influences on test performance are negatively or not at all associated with g loadings, whereas genetic influences are associated strongly and positively with g loadings.

It has been repeatedly shown that black-white differences on IQ test batteries generally satisfy the requirements of measurement invariance (Keith et al., 1999; Dolan, 2000; Dolan & Hamaker, 2001; Lubke et al., 2003; Edwards & Oakland, 2006; Trundt, 2013).

He could, of course, aver that his X-factors are so subtle that they would not violate

As Wicherts et al. (2004) point out, the fact that black-white IQ differences are associated with measurement invariance while the Flynn effect is not indicates that the two phenomena are separate, and that one of them does not tell us anything about the other.

One of the principal targets of Kaplan’s article are two studies by David Rowe and colleagues (1994, 1995).

Kaplan wrote " But positing, without any evidence, systematic differences in
hundreds or thousands of genes of small effects is surely no more plausible than
positing multiple environmental differences with small effects! as noted above, we do know of some environmental differences between the populations that are verifiably associated with differences in performance on IQ tests and related measures; we know of no genes that are so-associated."
Obviously he's not read Ward et al.'s replication of Rietveld's 3 alleles, nor my work on polygenic selection (
https://drive.google.com/file/d/0B7hcznd4DKKQWWNKU3pPbW1lS2M/edit?usp=sharing)

I also have a few rather minor objections: 1) the dig at philosophers near the end is accurate but unnecessary and should be removed; 2) "HM" is close to "Herrnstein & Murray" and could lead to some confusion; 3) the review of what phenomena are Jensen effects could be more thorough.

I was typing a long reply, answering the article, but now for the moment, I wanted to react on this. Personally, I would not say HM, but better HH, for hereditarian hypothesis. Alternatively if Dalliard still sticks with HM, perhaps use "H Model" instead. But in my opinion, it's not necessarily annoying. But of course, Herrnstein & Murray was the first thing that come to my mind as well. That said, the intro and abstract say clearly what HM is.

By the way, Dalliard, I have allowed myself to contact Kaplan himself. I think when we target someone in our articles, we should contact the targeted person and his works. That's the least we should do. I hope he will come here.

“Kaplan claims that the leading behavioral geneticist Robert Plomin has argued in his recent publications, such as Trzaskowski et al. (2013a), that the heritability of IQ is only in the range of 40 – 60 percent. In fact, Plomin has written that heritability in adults may be 80 percent, but that it is lower in children and adolescents (Plomin & Spinath, 2004). Trzaskowski et al. (2013a) analyzed a sample of 12 - year - olds.”

A more recent study is: http://www.nature.com/mp/journal/v15/n11/abs/mp200955a.html which found H² of 66% age 17. They cite more numbers in the 80% area in the introduction. Furthermore, as they note, the E (unique env.) includes measurement error and is usually not corrected for. Doing so increases the H² estimate a bit further (they cite a g reliability of .9). When discussing theoretical issues, it is important to correct for known errors in estimates cf. https://www.goodreads.com/book/show/895784.Methods_of_Meta_Analysis?ac=1

“It is important to understand that it follows from Turkheimer’s laws that proposed environmental effects on IQ are also expected to be confounded by genetic influences. Accor dingly, behavioral genetic research indicates that “environmental” factors , such as measures of family environment, child rearing style, and peer relations , are under substantial genetic control (Plomin et al., 1994 ; Kendler & Baker , 2007; Vinkhuyzen et al., 2010 ) .”

I would also cite this paper. I was under the impression that this was a major paper in this area because Gottfredson always refers to it as important.

Rowe, D. C., Vesterdal, W. J., & Rodgers, J. L. (1998). Herrnstein's syllogism: Genetic and shared environmental influences on IQ, education, and income. Intelligence, 26(4), 405-423.

“From these examples it is clear t hat racial disparities in encounters with the police do not constitute prima facie evidence of racial bias . Even if the police never relied on the ( generally reasonably accurate ) racial stereotypes about criminal offending, racial disparities in police scrutiny w ould arise because blacks are more likely than whites to engage in suspicious and illegal activities . The same inevitably applies to private security guards singling out seemingly disproportionate numbers of blacks for scrutiny . More generally, the observed black - white differences in crime rates are predictable from black - white differences in IQ and aggressiveness (Beaver et al. , 2013), and victim surveys indicate that the high arrest and conviction rates of blacks reflect their genuinely high rates of offending (New Century Foundation , 2005). T he common belief that a racially biased criminal justice system underlies the high black crime rate is difficult to reconcile with these findings .”

Beaver et al is a weak study to cite for this. Basically, they controlled for IQ and violent history and the race variable got a p value higher than .05. Big possibility of false negative here. But sure, not controlling for g is silly and is not evidence of any bias.

A good source for the accuracy of stereotypes is this chapter, which I highly recommend.

Jussim, L., Cain, T. R., Crawford, J. T., Harber, K., & Cohen, F. (2009). The unbearable accuracy of stereotypes. Handbook of prejudice, stereotyping, and discrimination, 199-227. http://emilkirkegaard.dk/en/wp-content/uploads/Todd_D._Nelson_Handbook_of_Prejudice_StereotypiBookos.org_.pdf

On the topic of pro-black discrimination. Jensen and others who have reviewed the bias literature (in the 80's) have noted that generally tests are not found to be biased against blacks, and sometimes found to be biased in favor of them (i.e. they don't perform as well as predicted). I don't know if still is still the case, but it is another small bias in their favor if it works on e.g. the SAT.

“American history offers an abundance of examples of how the prosperity of white - majority neighborhoods and even entire cities was destroyed as a consequence of large numbers of blacks moving in, indicating that white s’ (and other non - black s’ ) concern s about the character of their black neighbors are far from irrational.”

This is too inflammatory and doesn't even cite anything. I guess the most obvious example of this is Detroit, but I'm not aware of any actual study of it. The census data would enable one to calculate the average IQ and SD in IQ over time. So one just needs some historical socioeconomic data (crime, income, job, education) for the same area to compare with.

“Kaplan brings up stereotype threat (Steele & Aronson , 1995) as an example of a subtle environmental influence that can have a large effect on IQ scores, arguing that his X - factors could be similar in nature. However, stereotype threat is based on a causal theory of how anxiety about confirming a stereotype about intelligence hampers performance on intelligence tests. There is thus a direct and immediate link , supported by experimental evidence, between poor test performance and the proposed causal factor — so mething that certainly cannot be said of any of Kaplan’s far - fetched propositions . Furthermore, if Ka plan’s X - factors were real, their influence on IQ would have to be , for reasons discussed later in this article, far more subtle than that of stereotype threat .”

I would be more critical of accepting stereotype threat. Wikipedia lists quite a number of relevant papers here. https://en.wikipedia.org/wiki/Stereotype_threat#Criticism Stereotype threat is basically a priming effect in social psychology which has a replication crisis. e.g. http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0056515

“James Flynn has criticized researchers for assuming that racism is a magical ambient force rather than one whose possible effects are manifested through such ordinary mechanisms as poverty and poor self - esteem. Kaplan rejects this argument. Ind eed, Kaplan’s racial X - factors resemble nothing so much as magic. He presents no evidence for the hypothesis that “ racialized environments ” have an effect on IQ, and his evidence for the very existence of these environment s is very weak. Nevertheless, his model pre supposes that such environments, no matter how heterogeneous, act like magic bullets, causing large, g - linked cognitive deficits in blacks from all backgrounds while miraculously bypassing all the brain systems that mediate emotional and motivatio nal processes. Furthermore, the racial X - factors do all this in such a subtle way that no statistical signals of their presence can ever be observed, making racism a causal force completely unlike all known environmental influences on IQ scores. The essent ially occult powers that Kaplan attributes to white racism take his arguments beyond the bounds of science.”

But then again, the paper was published in a philosophy of biology journal, so in a sense it already is beyond.

I will give you the maximum, 5 stars, for the presentation of your article. It's so nicely presented... that's great. It's what I call perfection. Yes, literally.

Indeed, the black-white income gap is often reversed after such equating (Johnson & Neal, 1998; Nyborg & Jensen, 2001; Heckman et al., 2006), which may signal the presence of discrimination in favor of blacks.

You can also cite "Intelligence, Genes, and Success: Scientists Respond to The Bell Curve" by Devlin, Fienberg, Resnick, Roeder (1997). In chapter 9, "The Hidden Gender Restriction: The Need for Proper Controls When Testing for Racial Discrimination" (pg 200) you'll see that when controlling for age, IQ and parental SES, the BW wage difference vanishes, but that when they look at the relationship within each gender group, they see that black women are expected to have more wages than white females, while black men have less than white men.

Phillips et al. (1998) found that even after controlling for more than 30 variables related the economic, educational, cognitive, emotional, and health characteristics of parents and grandparents, about a third of the IQ gap in children remained unexplained.

It's about the chapter 4 of Black-White Test Score Gap, and the IQ test studied was PPVT-R. A vocabulary test. Perhaps precise it.

However, there is little evidence of their being overrepresented in relation to the black share of the perpetrators of crime

Shouldn't it be "them" instead of "their" ?

Specifically, the g loadings and heritability coefficients of tests have been found to be intercorrelated very highly, at close to 1.00 (Rushton & Jensen, 2010).

The R&J 2010 you cite merely cited an unpublished study by Jongeneel-Brimen & te Nijenhuis. Not published yet. te Nijenhuis gave me the draft (but in exchange I made the promise not to share it, so you have to wait for the definite version). Good article indeed, but needs more samples (Panizzon's sample can be added). In any case, I prefer to cite published study, rather than unpublished, if possible.

The principally genetic nature of g has also been confirmed in multivariate behavior genetic analyses where genetic influences on different cognitive abilities have been found to be largely common rather than ability-specific (Plomin & Spinath, 2004; Trzaskowski et al., 2013b).

The two cited studies talk about genetic correlation, if my memory is correct. Of course, genetic correlation always suggest the presence of higher-order genetic g, but it needs to be definitely confirmed through CFA modeling. Like I say, those studies you cite merely "suggest" the presence of g. If g is not modeled explicitly it can't be confirmed.

Kaplan uses Levene’s test for the equality of variances to investigate whether his simulated X-factors inflate IQ variances to a statistically significant extent.

To be sure, Levene's test is flawed. See here.

The predominant view among psychometricians and the one that is adopted in this article is that individual differences in intelligence can be conceptualized in terms of a factor hierarchy with a third-level general factor (g), second-level broad ability factors, and first-level test-specific variation (Deary, 2012). Higher-level sources of variation exert a causal influence on the lower levels of the hierarchy.

As for causal influence, it's only an assumption of the model, not exactly what it is tested. As I usually say, causality must involve a time trend, such as with longitudinal data. For example, Panizzon (2014) confirmed the existence of genetic g at the second-order level, but no causality can be inferred. Panizzon's study can't be used against van der Maas (2006) model for example. Although I (wrongly) used to believe that before. Because the others made silly comments about that they have found causal g or something like this. Just because they say it does not mean it's true.

As it happens, the variances of IQ scores in blacks are typically smaller than those of whites. Jensen (1998, p. 353) found that black standard deviations are usually in the range of 11–14 IQ points, with a mean of 12, compared to the white standard deviation of 15 points.

In Murray's (2007, see table 2) study of W-J cognitive battery, you see that SD of blacks is greater than that of whites. Why I am saying this is because Murray consider the sample he has studied to be the most representative of the US. Apparently, most (if not all) samples neglect lowest IQ portions of blacks, reducing their SD. But not in his samples. Of course, the samples amount to "only" 1669 blacks.

Accordingly, when Rowe & Cleveland (1996) fitted a biometric structural equation model to math and verbal test data from a genetically informative sample of black and white children, between 36 and 74 percent of the racial test score gaps was accounted for by genetic differences in the best-fitting model.21

No problem with R&C (1996). It's just that you should have added Brody's (2003) criticism to that study. See here. It's on pages 407-408.

it has consistently been found that environmental influences on test performance are negatively or not at all associated with g loadings, whereas genetic influences are associated strongly and positively with g loadings.

I will not be so sure. As you know already, see here, the evidence from CFA modeling is not compelling. It's only when you look at MCV and factor analysis or principal component that you see g is more heritable. But CFA is confirmatory in nature, which will differ with other methods, exploratory ones. Furthermore, unlike CFA, the MCV does not use latent variable approach. That's really unfortunate. That the 2nd biggest flaw in MCV. The first, biggest one, is that you can't test g-hypothesis against non-g hypotheses. There is indeed no way to assess model fit and see if the inclusion of latent g improves your outcome.

I say that for g-h2 correlation. However, that argument also applies for g and black-white difference, or any correlations between g and still other factors. As I know, the evidence in favor of Spearman hypothesis is positive but still pretty weak, because it relies mainly on MCV. And yet, MGCFA seems unable to confirm g hypothesis as the best model, but only that the g model fits the data no better (but not worse either) than non-g models (see e.g., Dolan 2000, Dolan & Hamaker 2001). Of course, when we look at the g/non-g factor(s) decomposition in g models, it appears that the weak version of Spearman hypothesis is true, thus confirming MCV. But this is still something different than model choice, which is based on model fit indices.

For g-h2 correlation however, we get the opposite. The genetic g model seems to have the best fit, but I don't see any proof from Panizzon that g is more heritable than the latent non-g factors. So, where's the Spearman effect ? Of course, there is still the problem of heritability dependent and independent of g, as you probably remember with our little conversation with Kees Jan Kan, but if we examine merely the h2, there is no evidence for Spearman hypothesis here.

It has been repeatedly shown that black-white differences on IQ test batteries generally satisfy the requirements of measurement invariance (Keith et al., 1999; Dolan, 2000; Dolan & Hamaker, 2001; Lubke et al., 2003; Edwards & Oakland, 2006; Trundt, 2013).

You should remove Keith, and Edwards/Oakland studies. They do not satisfy the basic requirements of MI, which require (1) pattern loadings, (2) factor loadings, (3) intercept. They have ignored testing the (3).

He could, of course, aver that his X-factors are so subtle that they would not violate

What is "aver" ?

As Wicherts et al. (2004) point out, the fact that black-white IQ differences are associated with measurement invariance while the Flynn effect is not indicates that the two phenomena are separate, and that one of them does not tell us anything about the other.

Disagree. MI, as I always said, is almost always misunderstood, probably because Wicherts and others do not describe MI very accurately. In fact, you can have violation of MI concerning FE gains at the subtest level and yet when you sum all of the subtests, you don't see test bias, because the subtests biases entirely cancel out (some biases against group1, others against group2). But in the work of Wicherts (2004) the subtest bias seems not cumulative, but cancel out instead (I reach this conclusion after my close reading, because this point is not even explicited by Wicherts). That unfortunately leads to several misleading comments on MI concerning the "role" of bias in accounting for the FE gains. If true, when "controlling" for bias, the FE gains should disappear. If not, all theories based on that assumption, such as the Brand's hypothesis or the Armstrong/Woodley rule-dependence model, all these theories should be discarded.

The best illustration you have, concerning Flynn gain, is from Must et al. (2009) "Comparability of IQ scores over time" (and Shiu 2013, who followed up the Must (2009) study). MI was violated, but the biases were not cumulative. Thus, illustrating the total irrelevance of bias to account for the Flynn effect.

If you want a proof of what you say above, you should better cite Ang et al. (2010, see figure 3), but certainly not Wicherts.
http://www.iapsych.com/iqmr/fe/LinkedDocuments/ang2010.pdf

Besides, if factor loading invariance is not respected, you can conclude that the differences are not directly comparable. For example, if in one group (1), the tests 1-4 load together, and form a verbal factor, and tests 5-9 load together to form a fluid reasoning factor, but in the other group (2), one or several tests, e.g., test 4 loads only on the reasoning factor, and the tests 8-9 load on reasoning as well as verbal factor, that is terrible. Because it means that tests 8-9 elicit verbal and fluid reasoning ability in group2 but elicit only fluid reasoning ability in group1. As for test 4, it means that group1 use verbal ability to resolve test 4 but that group2 use reasoning ability to resolve test 4. In case like that, the situation is just awful, and there is virtually nothing you can do about that. It's better to have intercept bias rather than factor loading or pattern loading bias.

One of the principal targets of Kaplan’s article are two studies by David Rowe and colleagues (1994, 1995).

One problem with Rowe's analysis is not, like Kaplan says, about statistical significance, but it is about measurement error. A lot of the reported correlations are close to zero, because they don't use latent variables. Is it possible that random errors also hide the race interaction ? Well, the problem is that I cannot reject that possibility. I think Rowe's need to be replicated using latent var approach. I don't remember if they have corrected for measurement errors or not.

I do not understand the " in your table 1.

What published study would you suggest? R&J 2010 is a sort of review article, so I think it's appropriate.

Of course, genetic correlations can be spurious (e.g., they may not reflect shared causal influences but common ancestry) but as they have been confirmed for g in multivariate GCTA with unrelated individuals, too, that's extremely unlikely.

Yeah, I think that study is more interesting for its methods than its results because of sampling issues. It should be replicated now that better data are available. I will remove the reference because it's really a rather equivocal study.

For example, the various Jensen and anti-Jensen effects can be readily explained by the g model, but not by non-g models.

MI comprises many stages, and it's still an analysis of MI even if not all stages are tested. But I can remove those two if you insist on it.

I take them to mean that because of measurement non-invariance cohort differences cannot be attributed to latent factors, whereas the b-w gap can be attributed to latent factors, given that MI is not violated. Do you disagree with this?

Of course, genetic correlations can be spurious (e.g., they may not reflect shared causal influences but common ancestry) but as they have been confirmed for g in multivariate GCTA with unrelated individuals, too, that's extremely unlikely.

I'm not talking about confoundings. Just that g must be modeled explicitly. What the studies are doing here is just a model with 2, 3 or 4, correlated factor models. Not g models.

Yeah, I think that study is more interesting for its methods than its results because of sampling issues. It should be replicated now that better data are available. I will remove the reference because it's really a rather equivocal study.

The sampling bias can be an explanation, but I remember several times I saw something like that. See Jensen's Educability & Group Differences, page 182, he reports some weird numbers on black twin heritabilities (ranging from 0.02 to 1.76). He said it's possibly due to low sample size. But too many times I read Rushton, Jensen, and Lynn, and others arguing about sampling issues in ethnic samples when white-group data differ from minority-group data. Of course, they are indeed smaller. But another possibility could be that the pattern of relationships found among whites are not necessarily generalizeable. This latter possibility seems to be somewhat obscured, more often than it deserves.

For example, the various Jensen and anti-Jensen effects can be readily explained by the g model, but not by non-g models.

Ok with that. But usually, the model fit has a purpose. It helps us to select the best model. So unless they are wrong in doing it like this, I'm not convinced that a g model should be selected. But if g model cannot be selected as the best model, how can we make claims such as "MCV shows that g1-loading correlate positively with group difference and non-g loading correlate negatively with group differences, and thus it proves that a g model fits better" ? Of course, if anything, this finding is more supportive of Jensen's view than otherwise. Like I said, I agree with that. But the selection of the best model is not a question for which i have found an answer already. But if I should trust what they (e.g., Dolan, Wicherts and others) said, then we still don't have a proof that g model is superior than non-g model, even though the parameter values of the g model confirm a Spearman-Jensen effect.

The Flynn 1980 is missing from the reference list.

The PDF file is strange in that copying text from it is somewhat buggy. What is the PDF creation procedure?

“One of the most important discoveries made by Arthur Jensen in his research on the black-white IQ gap was the finding that its magnitude is not invariant across different tests but tracks their g loadings, or correlations with the latent general factor of intelligence. In a meta-analysis of 149 tests, he found an average correlation of 0.63 between the magnitudes of black- white gaps and g loadings (Jensen, 1998, pp. 377–378). 9 What this means is that the better a measure of the g factor a given cognitive test is, the greater the black-white gap on it usually is.”

This is somewhat unclear. There were 149 subtests in total fifteen studies combined into one study.

Perhaps I am egotistic but I cannot approve of a paper on race differences in intelligence which doesn't even cite Piffer's work. This paper is not in touch with the most recent developments in this field such as Piffer, 2013 (https://drive.google.com/file/d/0B7hcznd4DKKQUTgyQXhwRmZTLVU/edit?usp=sharing)
or Piffer, 2014 (http://biorxiv.org/content/early/2014/08/14/008011).

Also, though I forgot to mention this, Jensen's estimate for r (B-W difference x g loading) = 0.63 is much too low. Applying meta-analytical corrections raises the figure substantially.

Wicherts makes no distinction (at least, not clearly) between subtest bias and test bias. The first does not imply the second, if there is DIF or DBF cancellation (DBF stands for differential bundle functioning, bundle is sometimes referred to subtest; yes, I know, it's truly annoying that people use different words and names to talk about the same thing). So, reading Wicherts, it says something like subtests 1-4 are biased against old cohorts, but 5-8 are biased against recent cohorts. Thus the subtests biases cancel out at the test level.

It seems to me that a lot of people using MGCFA are not aware of DBF cancellation/amplification. See here.

Roznowski, M., & Reith, J. (1999). Examining the measurement quality of tests containing differentially functioning items: Do biased items result in poor measurement?. Educational and psychological measurement, 59(2), 248-269.

They are not the first who make this argument. That said, it's only when I learned and read about DIF studies that I come to understand how users of MGCFA poorly understand the concept of bias. These are different things :

1. loading non-invariance
2. intercept non-invariance (difference statistically significant, through model fit indices)
3. intercept non-invariance (magnitude of the difference, needs to be calculated given the observed and expected mean difference)
4. intercept non-invariance (direction or "sign" of the bias)

Most of the time, when reading MGCFA studies, people just stop at 1. Sometimes, they consider 2. But almost never 3 and 4. They don't care or just don't know that "significant" difference is not equivalent to "meaningful" difference. Let alone the direction of the bias and the concept of amplification and cancellation DIF/DBF that is almost never discussed in their papers. But this concept is usually discussed in DIF studies.

This being said, things can be still different if Wicherts (2004) discovered in most studies that loading invariance is violated. But except for one study (the estonian data) it's usually the intercept that is violated (sometimes with residual invariance as well). See the models 2 with the lambda greek letter "Λ" (factor loadings). It's clear that it is not "Λ" that is source of problem.
http://wicherts.socsci.uva.nl/wicherts2004.pdf

I would say that it is only if most studies show violation of MI at factor loading level, that this claim can be more or less justified. Because it means that BW differences are comparable (groups use same ability to resolve the same test), but cohort differences are not (groups don't rely on the same ability), and thus any attempt to link BW gap and FE gains sits on a shaky ground.

Indeed, when they say stuff like "cohort differences cannot be attributed to latent factors" it's extremely confusing. They probably understand it as Lubke (2003) explained, i.e., it's about differences of the factors at work, as you also say in your paper. But the sentence seems to be more inclusive than just this idea. Still, I can agree if it concerns loading invariance. But if it's about intercept invariance, I cannot make sense of their sentence.

To illustrate, just look at Beaujean/Osterlind (2008). When "adjusting" for item bias, PPVT-R gains vanish but PIAT-math gain has been only cut in half. In the first case, you would say bias is an important factor, and in the latter case, you can say that bias can account for 50% of the FE gains. In the series of analyses performed by Wicherts, it's more like bias accounts for 0% of the FE gains, because the biases cancel out. And yet in both cases, because of intercept bias, the claim that "cohort differences cannot be attributed to latent factors" is entirely correct. For practical purposes however, it's completely irrelevant. It falsely gives the impression that bias fully or meaningfully accounts for Flynn gains.

Nonetheless, you can still ignore this comment here. It's not sufficient for disapproving your paper. I just wanted to make clear my views on this problem here. Perhaps it's me who's wrong. If you agree and add a note, that's excellent. Otherwise, no problem.