The Rindermann Reply

Identifying pseudoscience

Last year, Rindermann, Klauk and Thompson published a paper with a supplement about the intelligence test scores of modern immigrants to Germany in The Journal of Controversial Ideas. Paige Harden and I (this post is exclusively from me) wrote a critique of it. Since then, JCI published a rebuttal from Heinz Rindermann, and then Rindermann posted a really ugly piece about me personally. I am not going to reply to any of it point by point. (Among other things, the replies are just loooong. What is it about extremist argumentation that leads them to go on and on like that? I guess it is the Bannon strategy of flooding the zone with shit.)

Paige and I used two terms that I want to clarify a bit: pseudoscience (today) and essentialism (maybe over the weekend). They are both insults, and both hard to define. They can easily sound like name-calling addressed to ideas that one happens not to like. But Rindermann et al offers a great example of each of them.

In Rindermann et al’s analysis, they obtain “measures” (I am going to skip over a lot of egregious stuff that Paige and I already discussed in our reply) of brain-size and skin lightness by consulting reprints of old black and white shaded maps. They need to combine the two measures, so they announce:

In a factor analysis of the two evolutionary variables (skin lightness, cranial capacity), the first non-rotated factor, an evolutionary G-factor (big G for country), was used as a global indicator of evolution and ancestry.

To which we replied:

The “skin lightness” and “brain size” variables were then combined using “factor analysis.” We put “factor analysis” in scare quotes because the researchers did not perform the statistical analysis of variance-covariance matrices that commonly bears that name. One of the most basic rules of factor analysis is that any factor solution requires at least three indicators. Typing “FACTOR” in one’s SPSS code is not the same as conducting a meaningful statistical analysis. Their “factor” – essentially the median of two country-level ratings derived from the shadings of fifty-year-old maps – is what they variously call “evolutionary ancestry,” “evolution: G factor”, or simply “evolution.”

Here is what Rindermann says in the rebuttal:

[Turkheimer and Harden] assert firmly that factor analysis requires at least three variables. They do not provide any reasons or references for their assertion and, furthermore, their claim is not correct: In a factor analysis with two variables the loadings of the variables must both be fixed to 1 (assuming essential tau equivalence). The model is then saturated (df = 0; “just identified”; e.g., Geiser, 2023). The “holy book” of statistical methodology by Jacob Cohen and colleagues (Cohen et al., 2003, p. 473, Figure 12.5.2) gives an example of this (a latent variable with exactly two indicators), as does the more recent Backhaus et al. (2023, p. 417, their Figure 7.4). However, we have used here a principal component analysis for extraction. This also works without such restrictions with two variables. Nevertheless, the scientific gain compared to a simple item averaging (after z-standardization) for a scale is zero—the g-factor and the mean of such an item averaging correlate at r = 1. This also proves that the g-factor construction via the first unrotated factor is correct, but unnecessarily complicated. 9

In his usual roundabout way, Rindermann is saying first that two-variable factor analysis isn’t exactly wrong, in the sense that SPSS FACTOR doesn’t necessarily give an error report if you try it. His defense is that his analysis isn’t wrong; it is just meaningless. It is a degenerate case of factor analysis, in which you can manage to get an answer by explicitly not trying to estimate anything. The bolded part is strange— you have to remind yourself that when he says that the scientific gain of the analysis is zero, he is referring to his own analysis. As he does at several other places in the rebuttal (as when he abandons references to “evolution”) he is conceding that we were right. [OK, I can’t help myself. He also lets it be known that he wasn’t conducting a factor analysis, as he contended many times in the original paper; he conducted a principal components analysis. They are two different things, though I guess with two observed variables it doesn’t matter.]

But here is the point: why would someone do this? Faced with the need to combine two numbers, a job for which the “average” was designed, why would you announce that you were conducting a “factor analysis” producing a “non-rotated” factor? [Here I go again: You can’t rotate a single factor, even if you had more than two variables.]

The answer is, you would do it because you are a pseudoscientist. Pseudoscience is the meaningless manipulation of data in the service of an ideological goal. The Journal of Controversial Ideas let Rindermann et al get away with publishing this nonsense because the hocus pocus about non-rotated G-factors convinced a bunch of philosophers that something meaningful was going on. (I would still like to hear from one of the “distinguished scientists” and “statisticians” who presumably endorsed it.)

Next, I will talk about essentialism. Then, some thoughts about my tone when I respond to these people.