The working model for this kind of work is that a simplified model of human inequality approximately holds. In this model, every group of people has a distribution of and thus also an average value for human capital traits, chiefly but not exclusively intelligence. These distributions are primarily caused by genetic differences, as in, (true) polygenic scores (genetic potential) for the relevant traits. When people move around, they keep this genetic value, and this is true also for groups. In recent history (<100 years), the values are approximately constant though not in the more distant past (100 or 1000s of years). Thus, the basic prediction here is that if we can estimate this average human capital of particular groups, this should predict their performance when they move (migrate) or mix with others. Here one must take into account selection effects, that is, that migrants are not necessarily and not generally representative of the home habitat/country in these human capital traits. Thus, it is necessary to measure such selection effects. Following the initial work by the IAB on their brain drain dataset, I’ve used completed formal education level as a proxy for this. These estimates were generally obtained from ‘microdata’ (individual data) that were matched with the same cohort and age group at home (insofar as possible), counting only migrants who arrived as adults (25+), so that degrees earned in the host country are not counted. Thus, if a population at home has e.g. 10% of people with university degrees, but 70% of migrants have this, then they are very selected. The most selected corridors are:

Extreme selection is mostly seen for very poor origin countries, which is only logical, since the lower the education level in the origin, the larger the difference can be. Many poor countries have university degree rates in single digits, but manage to send people to the west with 50%+ such degrees. They are educating only a few people in university, and large numbers of them are leaving. People who are high human capital but leave their countries before taking education would thus generally be misestimated.

This kind of way of measuring selection only works for adults with completed education, a major limitation, so take it as a rough proxy and nothing more. It is possible to genetically measure the selection effects by comparing home/representative samples to migrant samples, though this has never been done systematically to my knowledge. This is generally because samples are too small or the current polygenic score estimates too imperfect (especially for non-Europeans). Performance of a given group in some host country is measured using whichever available social and cognitive data including employment rate, income, educational attainment, cognitive scores (e.g. PISA), crime, and social welfare use. Prior research has shown that it is not generally important which specific metric is used since the groups rank about the same across them. This working model is not entirely true, especially because some social metrics are strongly affected by age/sex composition (e.g. crime), time in the country, language/cultural distance (e.g. test bias). Thus, it is preferable to study 2nd and later generations. The problem with those data is in general that many countries do not provide useful data. This is especially true for people who change their citizenships, and children from mixed relationships (e.g. German mother, Spanish father). I have been inclusive and also used data based on citizenship when country of birth or parental country of birth was not available. This causes some biases since naturalization rates differ by group systematically: people from worse countries are more eager to convert to a new superior citizenship, especially because it generally means they cannot be deported (so easily). Countries also differ in how easy it is to obtain these citizenships (e.g. automatic at birth for many New World countries), which further adds noise and bias to the results. With these issues in mind, we don’t expect perfect results and neither do we find them.

So the basis of the analysis as of writing are data from these 34 host countries:

They are color coded by how much and how useful data they provide. In general, larger countries provide estimates for more origin groups owing to larger migrant populations. Countries with better government databases provide more data, insofar as the results aren’t completely censored/hidden. I have mostly obtained results from Western countries because these have high rates of immigration in the last few decades as well as useful public data. It’s possible there are more useful data to be found in e.g. Thailand. Belgium was the only western country I was unable to find any useful results for, perhaps a reader can find something.

The overall results for the origin countries should under the working model reflect the average human capital in the people from those countries, and the map we get looks like this:

Thus, it looks about the same as every other such map. Even after adjustment for observed migrant selection, Mexicans, South Africans, Indians do fairly well. You can click any country to see what data the results are based on. E.g., for Mexico:

So we can see that Mexicans don’t do well in USA or Canada, but do well in Europe. If you check migrant flows, something like 95% of all Mexican migrants live in the USA and are relatively unselected. A small number are in Europe, much more selected with resulting good outcomes. Depending on how you weight the results, Mexicans thus may obtain a large negative (if using migrant size weights), or somewhat to strongly positive score (if no weights). The overall models change somewhat depending on the weights, but not in a consistently obviously better direction, so I’ve used a middling approach to weights.

If we take the current ‘best estimate’ for each origin group and correlate it with national IQs (the best human capital measurement) or home country general development (HDI but better), we get:

And:

Thus, the main prediction of the working model is seen in the data. Results are not perfect, of course, given all the issues with the data quality, measurements, time-in-country, cultural/language biases in tests, and imperfectly modelled selection effects. But they are pretty good and compelling. Now no one can credibly claim that origin country metrics do not predict migrant outcomes consistently.

Most tests show male advantages, and only 3 show a female advantage, all of them quite small, below 0.2 d (multilingual vocabulary, color sorting, eye reading). By contrast, many of the male advantages are quite large, many above 0.5 d. These results thus suggest a general male advantage but focused on certain kinds of tests. The differences in these less general abilities than general intelligence are not surprising or new, though occasionally denied or questioned by feminists (e.g. male advantage in math). However, there is another potential explanation. The users on the site are obviously not representative but rather self-selection for high intelligence. It is possible that the male takers are more selected than the female ones.

To get around this somewhat I decided to analyze the large public datasets that the OECD has published from their PIAAC studies. This is the adult version of PISA. There’s data on 3 tests across 2 waves, and the gaps look like this, pooled across countries:

The difference in literacy was ~0, men scored about 0.20-0.26 better on math, and 0.08-0.10 d better on ‘problem solving’. Thus, again, consistent with a general male advantage. Obviously, the OECD aren’t big fans of Richard Lynn, so you can be quite sure they tried to get rid of these gaps in their item designs, but didn’t quite make it. For good measure, I ran my own item response theory models and checked for test bias, though it was quite minor.

The gaps also vary quite a bit across countries, wave 1:

Wave 2:

Insofar as age is concerned, the two waves don’t agree entirely:

In the first wave, the male advantage appears to be growing with age, but not in wave 2. I am not sure what would be the cause of this. Usually these kinds of abrupt changes are due to changes to the tests, mode of delivery, scoring, and not real differences. The datasets are far too large for these differences to be due to random sampling error. The cohort (birth year) gaps seen between the waves suggest a change in measurement or sampling.

From a Richard Lynn perspective, the findings aren’t that surprising in general, the male advantage overall would be quite small, an unweighted mean of about 1.5-2 IQ. His general proposed model concerns how to resolve the question of why we see a much greater male brain size, which is seen in every population, and which remains substantial controlling for height, with the known causal effect of brain size on intelligence, with supposedly no difference in general intelligence. This would only be the case if women have some compensating brain advantage, or men’s extra brain size occurs in areas unrelated to intelligence. As far as I know, there is no known candidate for such a female advantage, and brain imaging studies find that the entire brain, more or less, is involved in intelligence. So Lynn’s solution is that researchers had just made an error and men really do have such an advantage in line with the brain size advantage. This resolves the overall problem, but creates a new one. If men are smarter in general because of a larger brain, then why do we see such variation in the size of this advantage? It doesn’t make a lot of sense if this advantage has deep ancestral roots and should be more of a human universal than something that varies between populations and their cultures. I’m afraid I don’t know what the resolution to this question is.

Thus, about 28% of runs result in victory, which also varies a bit by character (highest is 30% for Defect, lowest is 26% for Regent). When playing, you are wondering what is the best decision to make in a given situation. By utilizing a large number of games, it is possible to give some causal answers to some of those questions. Each run also has quite a lot of randomness, so it is possible to score a given run for luck. Some card options are better than others, some relics worse than others. The top players manage to win nearly 100% of their runs, but average Joe not so much. The top players have built tier lists, so we can compare those to empirically obtained results.

Relics

First off, there’s primarily 2 things to look at: cards and relics. Both can be obtained from combat rewards, shops (by choice and availability), and events. The goal is to predict which build -- character+deck+relic combination -- wins. Starting with the simpler of the two, relics, the most obvious approach is to check which particular relics are commonly found in winning vs. losing runs:

But you can probably see that it’s a biased approach. The issue is survivorship bias. Runs that lose will end up with fewer relics since they miss out on opportunities to get more of them later in the game. It can also clearly be seen in the transforming relic Sword of Stone, which becomes Sword of Jade when 5 elites have been killed. Losing runs commonly die before doing so while winning runs do so, thus giving the opposite effects of the pairs. One can also see the bias by just comparing the relic counts:

So this approach will not clearly tell us what we want to know but we can get more sophisticated. What if instead of looking at finished games, we look at them at some earlier point, say, after the first boss (floor 17). This limits us to the runs that made it that far (64%) while keeping their relic variation and predicting the future from that point. This probably works reasonably well. Given the amount of data we have, we can also fit a single logistic regression with every relic in the game and by character:

We see some expected results. Skills are generally too strong in the game, and the relic that makes any acquired skill upgraded is a top relic for every character (Toxic Egg). And for a replication of sorts, we can do the same thing at another point, say, after boss 2 (floor 33):

The models additionally controlled for the difficulty (ascension) and player (fixed effect). Still, the models don’t guarantee a causal result because relics already picked up until that point affected the outcome. Some choice remains, and thus the possibility of confounding. Fortunately, we have some other options available. There are a number of different things that happen in the game that assigns a random relic to the player, which is thus uncorrelated with anything. Using this variation, we can see clearly. Random relics come from starting relics (Neow), elite rewards, chests, and some events. Each of these can be used to figure out the causal effect of each relic. The estimates they produce should agree with each other perfectly, random sampling error aside, and they seem to do so:

Here we see that the random relic models agree with each other relatively close to perfectly, while the cross-sectional data models even with controls are a little off. For some strange reason, Lava Rock random relics do not agree much with the rest. Based on these results, we can meta-analyze the signal from the different approaches to get a single best estimate for each relic x character combination:

Of particular interest are the boss/ancient relics, which are given after killing a boss. A particular ancient is shown and offers some relics in a limited pool. These can be relatively precisely estimated using the instrumental variables approach. Relics can only affect your winning chances if you are actually offered them, so we get the following causal path: offered -> picked -> win. The picking rates are affected by players’ choice based on their guesses about which relic gives the best winning chances, so it is not a clean causal estimate. However, the offers are random, so they allow us to get around this. This gives us the following results (pooled across characters):

It is likely that these differ by character but even 400k games is not actually enough to precisely estimate it, believe it or not. That’s because the outcome is a binary, and we need a standard error of, say, 2%points. This requires about 26,000 games with that character, but we have around 49,000 (for act 2) and 30,000 (for act 3), which are further split by the ancients appearing. More data is actually needed.

To be noted, shop-only relics are difficult to estimate. The only method I can think of is using the randomization from Lord’s Parasol (which gives every relic in shops). However, there weren’t enough runs to precisely estimate these.

Furthermore, some of the ancient relic options are not independent:

Thus, these present issues with estimation as there is never a choice, for instance, between X and X.

Cards

Moving on to cards, we can do the same thing as before. We can try the simplest model of comparing cards found in winning vs. losing runs. It gets more difficult here because decks can have multiple copies of a card, and they can be upgraded or not. I’ve decided to merge the data for the regular and upgraded cards to boost precision at some loss of detail. With enough data, one could separate the two, and figure out which cards are most important to upgrade. With regards to the counts, I’ve tried binary, count, and capped count approaches (deck has card yes/no, deck has X copies, deck has 0,1,2,3+ copies). The capped counts work best. The issue with the full count is that the rare boss/ancient relic Pael’s Growth makes it possible to clone cards, so a few decks end up with literally thousands of copies of some cards which mess up the results (meme builds). Anyway, these are the simplest results:

We can note a limitation of the data here, Mad Science is actually 9 different cards, but the save files don’t note which one is which. Most of the very bad cards are actually curses or quest cards (Lantern Key). We can also move on to post-beating boss 1 decks to avoid most of the survivorship bias:

It seems taking the Spoils Map is generally overly greedy, which is presumably why you often see the pros skipping it.

These estimates are still not entirely unconfounded, but we can utilize the final approach, which is to use instrumental variables for card rewards. Since cards can only affect your winning chances if you actually picked them, we get the following causal path: offered -> picked -> win. This allows the use of instrumental variables to estimate the causal effects despite players having a choice in what to pick. The correlation matrix for the card estimates across methods:

Aggregating the randomization-based estimations into a single best estimate, we can figure out that these are the best and worst cards for the characters:

Player choices

We have lots of data on what people actually pick in the game when given a choice. Usually, from a fight reward, 3 cards are offered but only 1 can be picked. So it is possible to rank cards by players’ preference. The simplest metric is just picked/offered ratio. More sophisticated is using 3+1 variant of the Elo rating. It turns out these produce about the same result, so it is not worth much except to highlight the value of skipping later in the game (the smaller your deck is, the more likely you will draw your best cards). Thus, we can compare players’ preference with our best estimates of what is best:

Relics are generally acquired randomly, so there is not much choice to look at. Except for shops and ancients where players choose themselves. So do players tend to buy the best relics?

It would appear overall players are fairly rational or tuned in to what is good. But critically, does it relate to player skill levels? We expect that the better players would buy the better cards and relics. To do this analysis, we have to estimate player skill. The model is: win ~ player_id + ordinal(ascension) + character. Using these, we can plot the buy rates vs. causal estimates as a function of player skill:

The findings confirm the expectation, higher skilled players’ choices correlate more with our best estimates 0.56 for high skill vs. 0.36 for low skill in case of relics. The difference is much smaller for cards, suggesting that the main separation between the good and the bad players is knowing what relics to buy in shops.

Conditional effects

The main issue with the above is that what is best for a build to some extent depends on what you already have. Some cards are good in all builds, while others are bad in some builds and good in others. The same for relics, though they are usually never bad for you (giving only positive effects, some exceptions like Royal Poison or Brimstone). Statistically speaking, such conditional effects are interactions, and we are not too keen on interactions on this blog. Still, there are surely lots of real interactions here, given that the very purpose of the game is to know about these and use them skillfully to win. There is, however, a severe statistical issue. With about 83 distinct cards per character, there are 3,403 different 2-way interactions to model for an exhaustive search (for a total of 17,015). Even limiting ourselves to within character combinations (it is possible to obtain cards from other characters as well as colorless/neutral cards), the combinatorial explosion results in severe statistical penalties for finding them. So we have to use a bit of theory or other empirical data to find them. Fortunately, we can use the winning builds data here. Each character has a number of primary build types, or archetypes. These can be statistically found by looking at the winning decks, in this case for Silent:

We see roughly the expected types: shivs, poison, draw/discard/sly. Most decks are not pure because it isn’t generally possible to win and never pick a suboptimal card in the final deck, and many cards seem to go in just about any winning build because they are just good overall (e.g. Adrenaline). A few also go into multiple (Reflex goes with Hidden Daggers). The results for Haze are based on the old version where it triggered on discard.

Based on these plausible pairs of cards, we can test all of these 2-way interactions specifically, and for each character. The model is: at floor X, after winning normal combat, conditional on already having X in your deck, does it predict winning chances to see Y? We call these positive interactions synergies:

All in all, pretty credible causal estimates could be made in most cases. The combinatorial explosion seen for cards prevents us from searching too hard, at least until more data is collected.

General findings

In general, the adjusted cross-sectional models agree pretty well with the randomization tests (IV or not), so in a way, using the more fancy methods was not necessary. This is of course only in hindsight we can say this. And the estimates don’t agree perfectly even after adjustment for random errors, so there is likely some confounding left in the cross-sectional estimates. We also confirm that our best estimates are more in line with what players do.

All the more detailed results for all cards and characters can be found on the site now.

The analytic strategy was about the same but expanded a bit:

1. We pick 3 random variables, set the first as the outcome, and the other 2 as the predictors, thus getting the general model Y ~ X1 + X2. This we test against the interaction model Y ~ X1 * X2. The variables are continuous variables, occasionally quasi-continuous, so we don’t have to use anything other than OLS

2. In variants of the above, we swap X2 for sex (binary), since sex interactions are probably those that are most common/largest.

3. We use LOOCV to assess how much variance the interactions add. This is probably better than trusting the analytic approximations (adjusted R²).

Alright, so did this dataset change the conclusions? Not really. We find just about the same as before:

Or if you prefer a table:

So in a sizable number, even a majority, of models the variance explained % gain was negative, which is to say that there was so little signal of an interaction that model overfitting caused the gain to be negative. Some somewhat sizable interactions were found in about 1% of the models. But if you look more closely at them, you can see the problem is not an interaction but that the main effects are misspecified as linear when they are really nonlinear:

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In real life, however, interactions are mostly not a real thing. This is despite their sometimes great intuitive appeal and well-known examples (e.g. mating success/attractiveness as function of height and sex and their interaction). So I decided to hammer home this message so that there is something robust and convincing one can refer to to prove the point. For this purpose, I reached for my trusty revolver OKCupid dataset. It’s very large, and has an extreme variety of items. Yes, it is from a dating site, but every other well-known finding I’ve tried replicating in the dataset worked fine. The very fact that it works so well, as do other convenience samples, is evidence against the importance of interactions. So here’s what I did:

1. Item-level data: pick a random ordinal variable as the outcome (Y), and 2 others as the predictors (X1, X2). Then fit the additive and interaction models: 1) Y ~ X1 + X2, vs. 2) Y ~ X1 * X2. Repeat 1000s of times. This approach needs ordinal regression since the outcomes are ordinal (all items have 2-4 answer options, which in the base case are ordinal or binary, sometimes nominal).

2. Scale-level data: aggregate items into scales from my recent 10-dimension model using a mixture of item types (binary, ordinal, nominal), then repeat the same approach as above using scales instead of items.

3. Scale-level data: aggregate items into scales that I had previously investigated in the cat-dog study, then repeat the same approach as above. The scales here are quite different from the ones above as they were handpicked to measure particular dimensions of interest instead of ‘falling out of’ the data.

4. Variants of the above swapping X2 for sex, to specifically look at sex interactions, the most intuitively plausible subset.

First we have to think of what we care about. The most obvious is to look at the p-values. This was the focus of the prior studies on interactions in this dataset. It is, however, a mistake I think. The dataset is so large that many terms reach p<5% even with tiny effect sizes. What we really care about is not so much whether there is literally any signal larger than pure noise, but whether these signals are of practical concern. For this reason, here we will focus on changes in model explanatory power, that is, R² values (which can be deceptive but bear with me).

Alright, so what was found? It can be summarized in a few ways graphically:

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Despite being based on a large international dataset, the dimensions are in fact not ‘supported by’ the data as such (in the exploratory factor analysis sense). They are just arbitrarily defined as the 2 factors from a curated list of items. You can read about that on the website for WVS:

The two dimensions have been created by running factor analysis over a set of ten indicators. The ten indicators used (five to tap each dimension) were chosen for technical reasons: in order to be able to compare findings across time, we used indicators that had been included in all four waves of the Values Surveys. These ten indicators reflect only a handful of the many beliefs and values that these two dimensions tap, and they are not necessarily the most sensitive indicators of these dimensions. They do a good job of tapping two extremely important dimensions of cross-cultural variation, but we should bear in mind that these specific items are only indicators of much broader underlying dimensions of cross-cultural variation [Source: Chapter 2 from Inglehart, R & C. Welzel. 2005. Modernization, Cultural Change and Democracy: The Human Development Sequence. New York: Cambridge University Press].

Since these data are publicly available, I decided to download them and try again using a theory-neutral approach. The WVS data has to be merged with the European Values Sutdy (EVS) to obtain data from the list of countries above (some European countries did not participate in WVS). After filtering to the common pool of items, we are left with only 44 common value items (asked in every country). Some items of high relevance are unfortunately missing, those dealing with homosexuality, because a few Muslim countries don’t allow researchers to ask these in surveys (shame on Egypt, Tajikistan, Uzbekistan, Iran). Moving forward with the 44 items with complete coverage for 92 countries (156,658 people), we can plot our trusty parallel analysis to get an idea of how many factors we could maximally extract:

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If you are familiar with personality psychology you know that there are endless debates about how many and which dimensions to rank people on. The Big Five (OCEAN)/5-factor model has been winning this battle for some decades, but before that it was Eysenck’s 3-factor predecessor, and before that Cattell’s 16 factor. Eysenck’s model has been mostly incorporated into the 5-factor model (except for psychoticism). Instead now we have the 6-factor HEXACO model, the alternative 5-factor model, as well as various simplifications, the big 2 (E+O, C+A+N), and the general factor of personality (GFP). However, I wanted to redo this work using the OKCupid data. This presented some interesting issues:

1. There is a lot of missing data because not everybody filled out every question, and some users specifically skipped some questions, or answered them in private (you could hide responses from others, so the scraper would not get them either).

2. The data structure is mixed. Many items are binary, some are ordinal (the options can be ranked from most to least something), and some are nominal (can’t be ordered). Analyzing mixed items is possible for factor analysis but requires specialized item response theory (IRT) models.

3. The dataset is large, so it took a very long time to fit the models, or impute the data. Like over a week even on a strong computer.

I had done some of this work years ago, and found the first few dimensions, but it was taking too long and I wasn’t happy with my methods. Fortunately, with the power of AI, I was able to revisit this question and get more decisive answers. Claude was able to rewrite the IRT software to use GPUs, which greatly sped up the model fitting time (by like 50x in core-time comparison but I have 16 CPU cores, so on average GPU was about 3x faster assuming full use), to the point where it was feasible to try out many models.

Generally speaking, we wish to know how many dimensions to extract. The standard answer in psychology is to use the various factor estimation methods with parallel analysis being the preferred option. The thing is that this always gives you a very large number when you have many cases because it is testing the actual seen structure vs. randomly generated responses. Just because parallel analysis or some other method says you should extract X factors (or the data supports it), doesn’t mean these are meaningful or reliably measured in that dataset. They may consist of just 2-3 items out of 100s. Since I wanted to make a practically useful test to put on the site, I wanted each dimension to be relatively reliable (at least .80) and rely on more than a few items. To figure this out, I explored 2 parameters: 1) the number of factors to extract (k), and 2) the number of items to use (p, in order of those with the most data in the database). Trying out the combinations of these values took a while (like 2 weeks on my strong computer even after changing to GPU fitting), but I am ready to present the results in brief. I guess I will eventually write up the full results, but building stuff with AI is much more interesting than writing academic papers, so I’ve been slacking off in that department (unlike the academics, I don’t have much financial motivation to write papers). So without further ado, these are the results for the estimated reliability of the least reliable factor as a function of those 2 parameters:

Alternatively, one can think of how adding another factor impacts the reliability metrics at a given item count:

Thus, in these data, the breakpoint is k=10 factors which is what I used for the scale on the site.

However, one can go further with the optimization. One doesn’t have to use the first p items from the site, but one can explore a larger number of items and pick an optimal subset. Thus, it becomes a variable selection problem after the exploration stage. Using the same criterion as above, I found that one needs about 200 items to reach .80 reliability for the 10 factors of interest. This approach explicitly uses cross-loadings to boost reliability. Most personality scales avoid items with cross-loadings because the scales were (and are) optimized using a simple metric of internal consistency, Cronbach’s alpha. This metric becomes 1 when every question is essentially a duplicate, which is why so many scales have many duplicate questions. This is very inefficient from an information gathering perspective. One would prefer quite dissimilar items that measure multiple aspects of personality at once. (I got this perspective from this blogpost.) This is what the OKCupid scale implements. My results look like this:

Some somewhat amusing results. This is largely because the scales are impure. There are multiple questions about guns -- this being an American test -- which tend to go with edginess. I’ve never even shot a gun, but still got a high score due to a fondness for inappropriate humor. Here are the top 5 most important questions for each dimension:

Casual-sex orientation:

Fitness & vitality:

2 questions are actually about transsexuals.

Sexual experience:

One question is actually about the user’s own fertility and another about potential partner’s fertility.

Guns and edginess:

Notice how 2 questions are actually about race and eugenics, not guns or crude humor.

Religiosity:

Social liberalism:

Yet another question about race.

Partner pickiness:

Some of these questions are quite sex-specific.

Intellectualism:

Questions concern sexual prudishness, self-rated intelligence, flag burning and so on. These items go together statistically speaking even if they measure seemingly independent things.

Kink and sexual exploration:

Substance use:

Overall we can say that these dimensions are somewhat unsatisfactory because they mix up different things. From this perspective, we should want to have more and more narrow dimensions. However, this conflicts with the goal of having reliable scales. A trade-off must be made here. You may have different standards than me. Factor analysis and scale construction remain somewhat of an art and not purely a scientific matter. The above is my best current attempt at getting useful dimensions out of the OKCupid data. Maybe in the future I will make another attempt. For now, let’s hope these dimensions are measuring important things and we will discover their correlations. If anything, they provide us with 200 questions from a larger pool, which could be analyzed in different ways for research purposes.

1. We don’t have many people who took all the tests.

2. We have severe sample selection bias, takers are far above average, and some tests have severe ceiling effects.

3. Tests vary in reliability, some are short, some long.

4. Tests vary in English ability dependency. Non-natives are not likely to perform at their true verbal ability level on a foreign language test, especially not vocabulary.

We can attempt to get around these problems by:

1. Using pairwise complete cases to estimate correlations among each pair of tests. From these we can build a reasonably full correlation matrix, which allows us to use matrix-based methods including factor analysis/structural equation modeling.

2. We can estimate sample selection bias, and attempt to adjust for ceiling bias.

3. We can estimate test reliabilities or use reference values and adjust for these.

4. We don’t have data on what language people speak natively, but we have IPs and thus can infer countries with some accuracy. Then we can assume that people in English speaking countries are mostly native speakers and those elsewhere mostly not. We can compare results.

Starting with (4), we can have a brief look if it even looks like we have to do anything:

So they are somewhat different, but not terribly so. The traditional metric for similarity of loadings is factor congruence which is 0.99. The one oddity is ICAR16 in full data vs. subsets. The reason for that is that ICAR60 has too little data for the subsets, so it is excluded and this artificially changes the g-loading since ICAR16 is a subset of ICAR60. Ideally, one would not include partial duplicates, but we can’t be too picky here. So maybe we don’t need to do anything for the correlations. The means, however, are quite different:

This is the familiar language and cultural bias, which is of course the largest on tests of such things, US knowledge tests. Curiously, the supposedly fluid intelligence test in UKBB shows a large bias. It’s a short time-limited test, so it indirectly measures English reading speed. The language-minimal tests (figures, ICAR, mental rotation) show quite small gaps as expected (except for number series, but it’s a tiny sample). We also get the expected finding that non-English speaking West knows more languages. This is also trivially true in the sense that English wasn’t one of the languages tested.

Regarding the pairwise complete correlations, they look like this:

These are the values used to do the factor analysis to get the g-loadings above. There is a lot of holes in this matrix, which one can either impute, or drop that particular test. A choice has to be made about how much to impute versus drop. A matter of researcher taste to some extent. The long vocabulary test with Prolific norms only has 4 correlations observed so far (it was posted yesterday), and it would be unwise to make much of those, though it does have a 0.61 correlation with Wordsum.

Hypothetically, the question we are asking is: in a dream world where all the tests are infinitely long and thus perfectly reliable (in classical test theory sense), and where all the test subjects are perfectly representative in terms of intelligence, and where every test has infinite range, what are the correlations among the tests? These are the values we need to get the true g-loadings. So since we have issues, we have to correct. Ceiling effects have a variety of existing solutions. Just for reference, this is what our Wordsum vs. American general population data look like:

25% of our online subjects got a perfect score versus 3% in the US White general population. It is easy to imagine how the correlation must decrease the bigger the lumping of scores at one end, since people of dissimilar ability are obtain the same numerical score. One simple solution I like is to bin the values and use the latent correlation from ordinal-ordinal or ordinal-continuous functions (polychoric/polyserial correlation). This can also be used to infer the split-half reliability estimate without bias from the ceiling, though it is still biased from the selection. Thus, to obtain an estimate of our hypothetically perfect correlation matrix we do these steps:

1. Ceiling bias correction via binning + polychoric.

2. Reliability correction (using value from split-half polychoric).

3. Selection correction

The latter is problematic to estimate. The value the statistical correction needs is the SD in our sample vs. population. However, the SD is affected by ceiling bias, which results in a far too small SD. This would mean the correction is too strong and correlations too high. Unfortunately, the only tests we have with truly representative samples for are the Wordsum and the Pew Research science, both which have severe ceiling issues for our subjects. We have data from the SAPA project for ICAR. The 16-item version is also affected by ceiling bias (15% in our data vs. 2% in SAPA’s). The people who took the time to take the full 60 item version are even more selected. I tried a variety of methods and they produced selection ratios of 0.50 to even above 1. I don’t know what the selection ratio really is, but I’ve used 0.70 in my calculations until we can find something better. This is what we get:

We have a number of too weak correlations, but that is in part because the raw correlations were close to 0 by sampling error. Corrections cannot fix this issue, only more data can. In any case, every correlation except for one (-0.05) is positive despite the sampling error. So finally, we get the answer for g-loadings we wanted:

Well, sort of. Some of the values are clearly wrong. ICAR60 is a long 4-part test, the true g-loading will surely be 0.90 or so, yet we found 0.54. Treat the above as minimum values more than unbiased estimates. These estimates are based on very thin overlaps due to small samples. As more data come in, we will be able to update these values. The most g-loaded tests are the usual quick knowledge tests. This is annoying because these are the most culturally sensitive, but on the other hand, they are fast and unstressful. This collection of tests also has too many knowledge tests, so the g factor will be somewhat colored, boosting their values slightly. As we accumulate more non-verbal tests, we will be able to fit more complex models to account for this as is typically done. We should then eventually recover the usual finding that fluid ability is the same thing as g on a theoretical level, though not using our observed scores.

Extras

The evolution of the correlation matrix for those curious:

First off, as AI wrote in the test description:

Political opinion is usually summarised as one line from left to right, and that line is real: Americans’ views on guns, welfare, abortion, race, immigration and defense all move together. But they do not move in lockstep. A factor analysis of 83 policy questions from the 2024 American National Election Study finds eight distinguishable dimensions, six of them strongly tied to the left–right axis and two — distrust of government and the wish to hand decisions to experts, business leaders or referendums — largely independent of it.

This test asks every ANES question that belongs clearly to one of the eight dimensions — 73 in all, in the ANES’s own wording — and scores you against the ANES respondents, weighted to represent US adults. A question that bears on two dimensions counts toward both. For every dimension and for the overall left–right score you see where you fall among all Americans and among self-identified Democrats, independents and Republicans, with the three parties’ distributions drawn on top of each other. The overlap is the point: on most single issues, a fair share of Republicans sit left of the median Democrat and vice versa.

The overall left–right score is a single factor fitted through all 73 questions: the one dimension that runs through the eight, scored directly from the items. In the ANES it correlates 0.80 with respondents’ own liberal–conservative self-placement and 0.77 with party identification. The questions are American; non-Americans can take it, but the norms describe where Americans stand.

So we begin with the 2024 wave of the ANES survey. It had 83 policy questions that we could factor analyze. Now, the thorny question in the years of latent variable modeling is how to determine the factor structure of some dataset. There are many methods for this: Kaiser’s criterion (eigenvalue > 1), MAP, model fit indexes and so on. The most popular is the parallel analysis. In this method, we simulate random but similar data at the same sample size and check their distribution of eigenvalues. We repeat this a number of times to get a distribution. Then we extract and keep all factors that exceed that value. For a very large dataset such as ours, this would mean keeping a large number of factors. First, the dataset correlations look like this:

Items are turned so that higher is the right-wing direction if any. This is because otherwise it would be more difficult to discern the overwhelming fact of such a dataset, namely, that most but not all questions load on a general factor. In intelligence data, this would be g, in political science, it is the left-right axis, which we would call leftism or conservatism depending on the direction and chosen framing. Applying parallel analysis to the ANES data we get this:

So parallel analysis tells us that the dataset can support about 15 factors. Model fit via RMSEA also shows that adding more factors does better. However, for practical purposes, we may not want just about any factor that can be seen. Even if they can be extracted, it does not mean they are meaningful or stable. So in my case, I decided to also require factors to be based on at least 4 items with salient loadings of >0.30. If not enforced, one can easily get factors that result from just 2 questions, which may just be oppositely worded repeats. One could have done this analysis differently and ended up with more or fewer factors. For instance, in the k=10 solution, race & gender grievances split into their race and gender parts, which may be important in some edge cases. In the appendix, there’s a bass-ackwards plot for those very interested. Anyway, based on my preferred 8-factor model, 74 items had a salient loading, 3 did not and were dropped, and 1 more item was dropped because of missing data (it was a near duplicate anyway). Of the remaining 73 items, they load like this:

These factors are themselves somewhat correlated, so one can factor analyze them again to get the second order general factor as in hierarchical factor analysis in intelligence. Their factor correlations are:

We can see that the 8 dimensions are correlated positively, though the last 2 much less so. I decided to score the general left-right axis from the 73 questions directly. This unconstrains the path from the general factor to the items to be more free. By looking at the plot above you can see that this makes little difference as the hierarchical left-right dimension correlates 0.99 with the one extracted directly.

Using this model, we can check the distribution of scores in ANES and from our test takers online:

Online takers are more bimodal but only for the 6 scales that have strong left-right loadings, and the last 2 are more unimodal, though not necessarily normally distributed. Finally, then, we can compare the left-right dimension the same way:

This is all well and good, but do these factor scores for left-right work? Well, I left out the self-placement items, so they could be used for validation:

People’s own ratings of their ideology and party allegiance correlate about 0.80 with the score. For the parties, apparently X and leans X are about the same thing. The gap sizes in these policy opinions are quite large:

As a function of age and sex, results are eye-opening:

In the US nationally representative data, men are more right-wing at a roughly constant effect size of 0.3 SD at all ages, and older people are more right-wing. In the online data, this pattern is extremely different before the age of 35. If one was only looking at online data, it would appear that young women have taken an extreme left-wing turn. I am not quite sure which plot is more realistic. The online sample is obviously self-selected but ANES-type data also suffer from low data quality as the takers are not very motivated. To note is that I only added the sex and age questions later so the full 28k dataset does not have this information, which may create further self-selection issues.

Appendix

Here’s a bass-ackwards type plot for the k=1-15 solutions with tentative labels (AI):

The p is the number of items with >.30 loadings. Some people were insinuating that I had deliberately merged nationalism with Israel love in some kind of neo-con plot. These people would perhaps prefer the k=9 solution where “Hawkish nationalism” splits the 10 items into global interventionism (Israel, Ukraine stuff) vs. domestic (border wall, voter ID etc.). This solution was not chosen because the technocrat factor declines from 4 to 3 salient loadings. If one added more or different questions to the dataset, one would of course get somewhat different factors. Factor analysis cannot find factors in a dataset that isn’t suitable for finding them.

• Arden, R., Gottfredson, L. S., Miller, G., & Pierce, A. (2009). Intelligence and semen quality are positively correlated. Intelligence, 37(3), 277-282.

• Pierce, A., Miller, G., Arden, R., & Gottfredson, L. S. (2009). Why is intelligence correlated with semen quality? Biochemical pathways common to sperm and neuron function and their vulnerability to pleiotropic mutations: Biochemical pathways common to sperm and neuron function and their vulnerability to pleiotropic mutations. Communicative & Integrative Biology, 2(5), 385-387.

Using the Vietnam Experience Study (US military veterans aged ca. 38), one of the only datasets that ever measured these two phenotypes together, they found correlations like these:

As far as I can tell, there is only one replication of this and it’s n=41 and didn’t find anything.

Since I have this dataset, I decided to look again. Arden et al did not show the scatterplot, but they should have because it looks like this:

This is the full sample, no adjustments or exclusions aside from missing data. The correlation is there, 0.14, vs. their 0.19, but if you look at the deciles on the right, you can see that the signal is entirely in the bottom 10% of men. This is more or less the case for every sperm metric that shows any signal:

Some of these metrics are interdependent since normal + small + large + tapered + amorphous = 100%. Thus, the simplest way to analyze that is just to use normal%.

So is this a real thing? Maybe the bottom 5-10% of men really do have quite a bit worse semen quality, or maybe there is some problem. Perhaps they were drunk at or before the testing, so their cognitive scores are bad and so is their semen quality. Or perhaps they didn’t stick to the rule of abstinence before ejaculation day. But before that, let’s examine the semen measures + covariates:

We can see moderate correlations among the semen metrics in an expected way. Factor analysis also confirms a 2-factor solution for volume and quality, so I will use those going forward. For good measure, here are the decile plots for semen quality and volume:

After looking closely at the 5% bins (not shown here), there is only an apparent effect in the bottom 10% of men sorted by g (intelligence), so I will use a binary for this group in the models. Here are some model results:

The results are pretty interesting. The bottom 10% men by intelligence have about 0.85 standard deviations worse semen quality, but only 0.35 SD less volume (p < 5% only). The quality link does not go away even with extensive controls, while the volume link became weaker and non-significant. The bottom 10% is only 48 men, so there is a limit to how much statistical precision we have to work with here, and we can’t say for sure about the volume. Note that Blacks have less semen volume than Whites, as may be expected by their smaller testicles -- a finding we previously reported from this dataset. Nothing predicts semen quality as well as low intelligence, though strangely abstinence predicts it mildly, perhaps not a biological link but a behavioral. A crude count of medical history (lifetime diagnosed conditions) predicts it slightly perhaps, while smoking, drinking, and BMI had no detectable effect. Concerning volume, abstinence is a decent predictor.

So it seems somewhat safe to say that intelligence does predict semen quality, but apparently only because the bottom 10% have really terrible quality. This is less easy to explain than positing some general fitness factor that underlies both, as done originally.

You can click any of the green cells to look at the scatterplots. For instance, French vocabulary (0-10 part of the 15-language test) and US-centric general knowledge test:

You can also discover weird stuff, like maybe Greek speakers aren’t very irritable (self-report):

I am trying to encourage users to take more than 1 test, so that the data can be linked. Many of these scales have never been studied together before, so new analyses become possible this way.

Have fun!

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A number of researchers have used these simple tests to examine various race differences. Lynn & Holmshaw 1990 reported these findings from South Africa:

350 black South African 9-year-old children were compared with 239 white British children on the Standard Progressive Matrices and 12 reaction time tests giving measures of decision times, movement times and variabilities in tasks of varying complexity. The black children obtained a mean IQ of approximately 65. They also had slower decision times and greater variabilities than the white children, but they had faster movement times. The magnitude of the white advantage on decision times was 0.68 of a standard deviation, about one-third of the white advantage on the Progressive Matrices. The result suggests that around one-third of the white advantage on intelligence tests may lie in faster information processing capacity.

Similarly, Lynn et al 1991 reported gaps in favor of Chinese (Hong Kong) over British:

239 British and 118 Chinese Hong Kong nine-year-old children, each representative for intelligence of Britain and Hong Kong, were tested on the Standard Progressive Matrices and on reaction times. The reaction time apparatus measured simple and complex reaction times proper (i.e., decision times), movement times, and variabilities. The results showed that all the reaction time measures were associated with intelligence and that Hong Kong children had a higher mean IQ and faster reaction times than British children. This suggests that the difference in mean IQ between Hong Kong and British children has a neurological basis. However, the British children showed faster movement times and lower variabilities, contrary to expectation. This suggests independent neurological processes may underlie reaction times, movement times, and variabilities.

And Lynn & Shigehisa 1991 (2nd study) reported that the Japanese also outperformed the British:

Japanese and British 9-year-old children were compared on the standard progressive matrices and twelve reaction time parameters providing measures of simple and complex decision times, movement times and variabilities. The mean of the Japanese children on the progressive matrices exceeded that of the British children by 0.65 SD units and on the decision times component of reaction times by 0.50 SD units, suggesting that the high Japanese mean on psychometric intelligence is largely explicable in terms of the more efficient processing of information at the neurological level. Japanese children also showed faster movement times but, contrary to expectation, had greater variabilities than British children.

The hypothesis that reaction times are positively associated with intelligence was tested on 444 nine-year-old Japanese children. Intelligence was measured by the Raven’s Standard Progressive Matrices, and 12 reaction time parameters were obtained to give measures of movement times, reaction times proper (decision times), differentiated into simple and complex reaction times, and variabilities. Factor analysis of the reaction time tasks indicated the presence of a general factor and three primary factors identifiable as movement times, simple reaction times, and complex reaction times. Of these, only complex reaction times showed significant associations with intelligence.

And it’s not just Lynn. Sen & Jensen 1983 reported that Americans outperformed Indians. Jensen & Whang 1993 examined White and Chinese Americans and found the Chinese did better.

Common to all the above studies is that they relied on various convenience samples, not large representative samples. Given the consistency of the results, we aren’t really in doubt that the larger representative samples would replicate the patterns, but nevertheless, it is good to know for sure. I recently found that there is reaction time data from the simplest version available in the NHANES III (1988-1994), a large representative American sample of older people. NHANES in general are a goldmine because they are completely public and have many interesting variables. Unfortunately, the older datasets are only available in the obnoxious fixed-width data format that was commonly used for recording data on tapes (as it is very compact). Modern AIs have made accessing and using this data much easier, so now I can quickly do an analysis that would otherwise have taken many hours. In the dataset, subjects took the simple reaction time test 50 times, so each person has 50 values available. The distribution of which can look like this:

These are from the first 9 subjects with data (only adult subjects took the reaction times as part of medical examination). Note the shapes of the distributions differ, and the presence of outliers (3 subjects have inattentive trials at 1000+ ms). There is also a learning effect, which we can see if we plot reaction times as a function of trial count:

Most subjects get better with practice, but some appear to get tired or bored towards the end. One could fit individual learning rate models to the data, but from the data you can see that these models would give rather nonsensical results in many cases. Bottom left subject appears to be learning if one looks at the red line fit, but not really, just their first trial was extremely slow.

Most of the studies above reported various summary statistics by race. The analytic choices are actually nontrivial because we have 2 decisions to make regarding summary statistics to use: 1) within-person, and 2) between-person. For within person, I can think of a number of options depending on what we care most about. It is known that the dispersion (variability) of the distribution is itself indicative of cognitive ability. The presence of severe outliers means we should also explore robust statistics, or use exclusion rules. I’ve opted for the simplest approach of including all data, so if subjects were inattentive at first, or bored at the end, this is part of their real performance, just like they might be inattentive or bored when driving a car. For the choice of summarizing between-persons, I’ve used the mean. We can judge to which extent that is sensible by looking at the distributions of the various within-person metrics by race:

All the between-person distributions have the same kind of right tail as they do within person. Thus, using the mean is somewhat misleading. The distribution doesn’t appear to differ in shape by race however. In every case, the Whites (European Americans) do better, which we can see (barely) by the blue lines being taller and towards the left (more clustered at faster reaction times). If we nevertheless use the means to summarize the distributions, we can calculate the familiar Cohen’s d gaps here in terms of the White between-person SD for consistency. In general, Cohen’s ds are calculated using average SDs or occasionally using the total sample SD. The latter is more inappropriate as the presence of ethnic diversity increases the total sample SD and reduces any Cohen d gap sizes (for instance, Wechsler’s SD are based on total sample SDs, so their IQ gaps shrink as the norm sample becomes less White over cohorts resulting in a phantom gap narrowing). However, to keep things most consistent, I’ve long decided to report all Cohen’s d’s using the White SD, so that the reference population stays the most consistent between samples and studies. With that said, here are the gaps on these metrics:

So despite the data being somewhat irregular, it doesn’t matter too much whether we try to deal with this or not. The Black-White d gaps are 0.57 for a mean, 0.51 for the median, 0.57 for the mean of the slowest 20% trials, 0.41 d for the fastest, 0.41 for the standard deviation (SD), 0.49 for the robust version (MAD), and about 0.30 d for 2 other metrics. The Mexican-White results tell a similar story.

Finally, though the samples were pretty representative, we can adjust for age and sex, the Whites were older, which goes against them slightly, and there is even a temperature measurement of the room, which turns out to be surprisingly important:

Taking into account these factors (lest someone claims that maybe the non-Whites did poorly because of lack of AC communism), we can use this model: metric(RT) ~ race + spline(age) + sex + room_temp. This gives us these results:

So in line with slight age confounding (Whites are older and older people are worse), the gaps are somewhat larger after the adjustment. In general, it made little difference.

Finally, NHANES 3 administered a number of other tests, though not to each age group, but we can still compute the Cohen’s d gaps for each test:

The other tests also show sensible gap sizes, some of them even exceeding 1.0 d. This is somewhat suspicious, but for the Mexicans, it probably has to do with language. NHANES has a question for administration language (recall, this is in the 1980s), so we can split by English vs. Spanish:

The results somehow make less sense than before. The gaps on reaction time are also much larger when using Spanish as administration language, even though language cannot affect performance on a simple reaction time test. This thus suggests that Spanish language is more a proxy for something else that is going on here. This oddity aside, overall, the results were normal for the reaction time gaps in general. The R notebook is available here.

In German, it shows the performance of Turks on PISA math by year and destination country. It can be seen they all cluster and show no improvement over time. The natives are slowly declining in the comparison European countries, presumably because the ‘native’ category increasingly includes non-Europeans.

Since the PISA data are all public, we can redo this exercise but expand it to be worldwide. From a human capital perspective we can think of the world as a migration matrix of performance. Columns can be destination countries, and rows are origin countries, and each cell has the mean score seen on PISA. In an ideal world, we would have this complete matrix, but due to sample size limitations in PISA studies, privacy protection (not all origin countries are listed), unequal population sizes (larger countries can send more migrants), and differential migration (some countries send more migrants per population size), we end up with this matrix:

To give some examples:

• Turks in Austria (413), Germany (427), Denmark (424), Switzerland (447), Belgium (430), Netherlands (460), Finland (416), Liechtenstein (471).

• Indians in Australia (549), Canada (515), UK (510), Brunei (509), New Zealand (527)

• Chinese in Macao (542), Hong Kong (549), Australia (583), Canada (603), New Zealand (577), Kazakhstan (433), Finland (488), Panama (401), Netherlands (519)

These are all PISA math scores listed in order of largest samples (e.g. only 60 Chinese in Panama). I have analyzed the reading and science as well, but math seems the least prone to language bias in theory, so we will stick with it.

The simplest model we can posit is that migrants perform as they do at home, and they stay at that level. This is essentially the strict global hereditarian model. In this simple model, the score means are identical in expectation no matter where a given group of people are located. Insofar as this is accurate, it is a simple matter of predicting migrant performance since we can simply regress it on the national IQ of their home country:

We see that several countries don’t participate in PISA but send migrants (marked in red), so their home PISA scores were imputed using the NIQ converted to PISA scale. India is the biggest outlier as they perform far better in non-India than they do in India. This suggests that Indian migrants are either not representative or India’s IQ is severely underestimated. However, let’s first consider the next simplest model: score ~ origin + destination (dummy). In this case, we allow for the fact that some countries are better at integrating migrants in some way that affects PISA scores. Positive values for the destination dummy thus means that migrants in that country perform better than expected by the origin countries’ NIQ. I would show these models but given that it is just 2 sets of values by country, it is too long to show. I can show the simplified model where we use the NIQs of the country as stand-in for the relevant values. Thus, each subject has an origin NIQ (the mean of their parents’ values, or if there is only 1 parent origin listed, that parent), and the NIQ of the destination country: score ~ origin_NIQ + destination_NIQ + year:

Thus surprisingly, perhaps, we see that destination NIQ is a much better predictor of how migrants perform on PISA than their home country’s NIQ according to the standardized betas. For the model with dummy variables, it is possible to compare the joint effects of the dummies for destination with the origin effects in terms of r2, so that we can get an idea of what is more important in the broad perspective:

Both approaches tell roughly the same story in that destination beats the origin as a predictor, whether we let both ‘roam freely’ or force them into NIQ terms. So what is going on? It’s our old friend the migrant selectivity issue. We can compare the origin effects versus the migrant selection index which we can calculate from the IAB Brain Drain database. This database contains information about the educational level (3 classes) of people who left various countries and migrated to the OECD. Using this, we can compute a selectivity index by comparing highly educated % among the emigrants vs. the country for the same year and age group. Then we get this result:

Now things make sense again. The countries that send relatively elite migrants compared to their populations are the same ones that perform well on PISA in other countries. If we don’t add the destination country dummies, we get a weighted correlation of 0.73 and 0.77 if we control for destination country even if this is uninterpretable. From a statistical perspective, this is somewhat of an annoying approach because we now have a complex 2-level model:

• score ~ destination + origin + year + residual

• origin ~ migrant_selection_index + residual2

India is the biggest outlier, Indians around the Western world perform roughly at 105 IQ on PISA math given an origin NIQ of 76 or so. This is close to the other results seen for Indians in the USA in my prior post. Note also that other countries show interesting selection effects. Pakistanis are also selected, just less so than the Indians, and they end up underperforming the Europeans despite the selection. Possibly with stronger selection, the UK wouldn’t have so big a discussion about the grooming gangs, though I suspect a lot of this difference has to do with the additional factor of Islam vs. Hinduism.

There is a way to simplify the models above into a single model, namely by converting origins to origin_NIQ expectation, destination_NIQ and then adding the selection index. Furthermore, we can exploit the fact that selection index differs also by destination, not just origin. Thus, we compute every origin x destination selection index and use this. Thus the model becomes:

• score ~ origin_NIQ + dest_NIQ + selection

Here’s the models using natural units slopes:

Reading the table takes some care. In the first model (O), we only use NIQ of origin as the predictor. The expected value begins at 65 IQ (in PISA units but here converted to NIQ), and rises 0.34 for every IQ point in the origin country. It’s not a great model, 12% variance. This model would predict, for instance, that a Dane in Sweden would get a score of 65+100*0.34=99, which is about right. A Somali in Denmark would get 65 + 70 * 0.34 = 89 IQ, too high. The second model (D) uses only the destination country IQ. Strangely, it has a slope larger than 1 and combined with a very negative intercept. Thus a Somali in Denmark is predicted to have a score of -86 + 100 * 1.86 = 100 IQ. In fact, it just predicts ~100 IQ for any migrant in Denmark or any other Western country. Models with S show that the slope for selection index is about 4 IQ/logit of selection (3.6 to 4.6). Curiously, destination IQ combines poorly with selection (model D+S), but origin + selection (O+S) is almost as good (65 vs. 69%) as the full model (O+D+S) despite the fact that destination beats origin alone (models O vs. D). In terms of parsimony, then, we could use the O+S model. This is what it predicts vs. what we see:

Looks pretty good, and this model essentially only uses the origin IQs and modifies them by the degree of selection we estimated using the independent Brain Drain dataset.

Referring back to the diaspora vs. home NIQs, readers may have noticed the unusual result that Americans underperform. Their mean PISA math outside the USA was only 440, on par with Portugal. Why is that? Performance by destination:

• Israel, 102 IQ, American Jews moving to Israel

• Canada, 102 IQ, Anglo-exchange

• Australia, 100 IQ, Anglo-exchange

• Mexico, 70 IQ, Mexican returnees

• USA (home), 97 IQ

The small numbers of Americans (50) who presumably returned to Mexico did extremely poorly and pulled down the average, and because it was using inverse-variance weights (like in random effects meta-analysis), it had a disproportionally large effect. The weighted mean is 480, which is not so far from expectations.

Another visible outlier in the plot is PHL or Filipinos. They scored about 100 IQ outside of their home country. PISA does not provide any ethnic data, but it does provide home language. Of the Filipinos migrants, 56% speak English at home even when they move to non-English speaking countries such as Macao. They bring English with them as the premier language and it isn’t just assimilation. In contract, of Filipinos living in their home country, only 7% speak English at home.

Concerning the Malaysians (MYS), 39% of the migrants speak Chinese (Mandarin+Cantonese+other Chinese) at home, but it’s 23% of Malaysians, so close to 2x the rate. Another 32% speak English at home, which is uncommon among normal Malaysians. Reversely, we can say that about 70% speak Malay at home in Malaysia, but only 21% among the migrants.

One can keep going through the outliers to attempt to figure out a plausible story of what is going on, but I’m not too interested in the particular cases, but in the overall pattern of results.

Regarding the math vs. other domains, here’s the O+S models for the others in comparison:

Thus surprisingly, perhaps, it turns out that the weakest model is the one with math as the outcome, the other 2 domains give somewhat stronger model fits as does the composite (average) score. The PISA people pretend that their tests are measuring 3-4 related constructs, but their scores correlate on average 0.89 with each other, so they are effectively unidimensional measures of some kind of scholastic-colored g factor. See Pokropek et al 2022 for more on this.

Conclusions

• PISA worldwide data can be used to study country of origin effects with regards to national IQs.

• However, due to biased data coverage, only 2.2% of possible origin-destination pairs have at least 25 students, so interpretation is difficult.

• It turns out that emigrant selection is the major factor explaining differences from expectations, especially because Indians overperform compared to Indians at home.

• Using just NIQ of origin + selection index explains about ~70% of variation in migrant PISA performance.

Yes, I could have included more databases, but AI tells me these are the most commonly used, and for the approach I develop below, it would not matter much to include more. The next step is to count the number of top universities by country. If we arbitrarily pick top 200, then we get the following top countries:

The results are reasonably, but not perfectly, correlated. USA has the most top universities in each database, but is the number 45 or 62? Asian countries show extreme divergence, South Korea has between 1 and 7 depending on the system. Which numbers are more sensible? It’s not obvious. Either China has already overtaken the UK (ARWU) or it is still far behind (QS and THE). Thus the main problem with the above findings is that we have 3 different databases of university rankings, so how are these best combined? Rank-order data is limited because we can’t say how much better rank X is than X+1 or X-1. We need interval data. Fortunately, it turns out the methods for computing these rankings are public and so are the underlying quantitative indicators. Thus, we can treat this as an ordinary factor analysis problem. We simply pool the available indicators and see what their correlations look like:

We unsurprisingly find a positive manifold, every quality indicator relates positively to every other indicator. The pattern is not that great though, there are a number of very weak indicators with correlation down to 0.08. This does not appear to be a bug, it’s just a bad measure, at least insofar as any general quality is concerned. Given the positive manifold, we can at least pragmatically treat the data as being explained (reflective) or well-summarized by (formative) a general factor or index, and then score every university on this university-g scale. Technically, the g here only refers to it being the general factor of these indicators of university quality, but you could also think of it as a proxy for the average human g -- general intelligence -- at the universities, or just think about it as university goodness. We also notice in the correlation matrix that some variables are near duplicates, which will inflate the variance related to that specific aspect of university quality. For instance, there are 3 closely related variables across 2 databases of internationalization, students/faculty/outlook, the latter which includes the former as well as international collaborations (joint authorships). Decent to half-decent arguments can also be made against each of the indicators as potentially measuring something other than university quality (number in parens is their assigned weight):

• Alumni (10%) — “The total number of the alumni of an institution winning Nobel Prizes and Fields Medals.”

• Award (20%) — “The total number of the staff of an institution winning Nobel Prizes in Physics, Chemistry, Medicine and Economics and Fields Medal in Mathematics.”

• HiCi (20%) — “The number of Highly Cited Researchers selected by Clarivate.”

• N&S (20%) — “The number of papers published in Nature and Science between 2016 and 2020.”

• PUB (20%) — “Total number of papers indexed in Science Citation Index-Expanded and Social Science Citation Index in 2020.”

• PCP (10%) — “The weighted scores of the above five indicators divided by the number of full-time equivalent academic staff.”

• Teaching (30%) — the learning environment: a reputation survey plus staff-to-student ratio, doctorate-to-bachelor ratio, doctorates-awarded-to-academic-staff, and institutional income.

• Research (30%) — volume, income and reputation: a research-reputation survey, research income (scaled to staff), and research productivity (publications per staff).

• Citations (30%) — research influence: captures how often a university’s published work is cited by scholars globally.

• International Outlook (7.5%) — staff, students and research: the proportion of international students, the proportion of international staff, and the proportion of papers with at least one international co-author.

• Industry Income (2.5%) — knowledge transfer: research income an institution earns from industry, scaled against the number of academic staff.

• Academic Reputation (40%) — based on a global survey asking academics to name the institutions where the best work is being done in their field.

• Employer Reputation (10%) — based on a survey asking employers to identify the institutions producing the best, most competent graduates.

• Faculty/Student Ratio (20%) — the number of academic staff relative to students, used as a proxy for teaching capacity.

• Citations per Faculty (20%) — total citations to an institution’s papers over five years, divided by its number of faculty.

• International Faculty Ratio (5%) — the proportion of faculty members who are international.

• International Students Ratio (5%) — the proportion of students who are international.

You can make arguments against each of them. Alumni measures raw counts, so just having more students in general will make these numbers higher. A small, elite and focused university is beaten by one with more students. Award measures ability to hire expensive staff, so one can consider it a measure of wealth of the university. Citations per faculty punishes hiring teaching focused professors. The ideal university by this metric has 0 students and 3 top researchers. Internationalization metrics punish larger countries since they have an easier time collaborating within country (USA, China), and one submeasure rewards joining papers with 100+ authors. It can also be gamed by intentionally attracting foreign students, even if these are below average. This is a typical strategy for many UK universities I’ve been told. Generally, though, gaming all metrics at the same time is not so easy, so their joint effect is probably a fair estimate of the general factor.

There are various ways to deal with such overlapping or strong group factors. One common approach is to score the data using the bifactor model. In this case, we posit that a few underlying unobserved (latent) variables cause the pattern we see. One of them we posit is general, so it affects every indicator, whereas the others only affect some subset (the group factors). In our case, we can fit this model:

The uni-g has reasonably high omega h. But some of the other factors are not that great, especially not the last one which only has 1 indicator loading at 0.45. However, it doesn’t really matter much because alternative models produce essentially the same score estimates with correlations all above 0.99. Even just taking the mean z-score of variables (so called unit-weight factor analysis) correlates ~0.97 with the factor analytic scores. Thus this single score represents the quality fairly well as a single dimension and with that we have a single number for each university in this joint database, 621 universities that were included in each of these databases. However, there are many more universities in the world, and this is important as we shall see later. Here’s the sample sizes by database unions and intersections:

Above we used the full intersection to get the 621 universities with full data. However, given the strong correlations among the variables, we can also make reasonable estimates of uni-g for the union of all 3 databases using whichever variables are available. There are different approaches here, but a simple and principled approach is to fit the 1-factor EFA model using FIML which uses the available data and provides scores for every university. I tried alternative approaches such as building subset specific regression models, but the results were correlated 0.99 or so. Thus, we have obtained uni-g estimates for 2000+ universities.

Having integrated our estimates into a single best estimate we move to the next problem with the university counts by country: having more people in your country means you have more universities, and thus more chances to have top ones, even if there are no average quality differences between countries’ universities. Here are the correlations across different thresholds for “top” university:

If the question is just who has more top universities, and thus where global research talent is concentrated, then it will tend to be whichever country has a large population, a good human talent average, as well as suitable political conditions. There are also historical lags, as new talent moves towards existing talent clusters, so even if some countries no longer have good political conditions (like the UK), then they can rely on the system’s self-reinforcing feature for some time. If the question is instead who is good at making top universities in relative terms, then we have to use some kind of the dreaded per capita analysis. Ignoring those other factors for now, here are the by country counts using the final model for the combined dataset and the per-million rankings for top 200:

USA moves from global 1st to 16th. In other words, America doesn’t actually produce a lot of top universities taking their population into account using the naive approach.

The problem with per-person estimates for rare cases is that the estimates are very unstable. A small country like Iceland (400k population) might have a good university or might not, just like it might have a single Nobel Prize winner or not. A single positive observation would result in a very high per-person rate (2.5 top universities per million people) and 0 positive observations would result in the lowest rate of 0 per million. Hypothetically, if we were to magically scale every country’s population to 1 billion, we would learn the true rates without uncertainty, and this true rate would lie far from the observed rate. In other words, for rare cases/events, it is impossible to even arrive at a correct estimate as any observation would lead to a very wrong result compared to this counterfactual. The general solution to this issue is to use better models. There are two main approaches. First, we can adjust the observed per-person rate towards a plausible value, typically the global mean (weakly informative prior) using something like Empirical Bayes. Second, we can use count models to predict the expected count for each country as a joint effect of the variables we use for prediction + population size. This latter approach fixes the standard errors at the cost of interpretability of the model results. Yes, I know, some will object philosophically to this statistical approach. There is only 1 Iceland, and it only has the current number of top universities (0), so its observed rate is the true one. From this perspective, there is no possibility of estimating model uncertainty because we already observe all the data, it’s not a sample but the population. This means there is no point of doing any standard errors or inferential statistics at all. While perhaps philosophically defensible, no one actually follows this approach in practice. Everybody reports p values for regressions for US states, even though we also observe all 50 of them, and not a random sample of 50 states from a hypothetical infinite rerun of US history where they would be different numbers and kinds of states. But I digress. Anyway, in our list above, the 4 last entries on the per person list have exactly 1 university in top 200, their country’s top university.

Concerning the causal explanation of the worldwide distribution of universities and their quality levels, one could of course take many approaches. I posit that the most foundational approach consists of 2 root causes: national intelligence average (national IQ, or NIQ) and the population size in a distributional model. NIQ and population size are not closely causally connected. My causal model of the data is that given a sufficiently large population size (say, 1 billion), every country would have a distribution of universities with a mean uni-g of some value. The population size affects the number of universities but not mean uni-g. NIQ affects both the mean uni-g and the number of them. Thus, it moves the distribution towards the higher end of the university quality dimension and makes it larger. In theory, then, if we measured all universities in the world, then NIQ should be very highly correlated with mean uni-g for the country, since this is not affected by population size. However, the university databases do not measure all universities. There are about 20k accredited universities worldwide of which we observe data for about 2000 or 10%. The problem is that we are measuring them from the right tail, best first, so not a random sample. Thus, for countries with medium to low mean uni-g, we don’t observe the entire distribution of their universities so their mean uni-g will be inflated by sampling bias. For instance, Denmark has 7 broad universities, 3 are in top 200, 6 in top 500 and all 7 in top 1000. Adding more universities to the database would thus not expand this list and Denmark’s uni-g mean would remain unchanged. However, adding more universities to the database would add many more for India, Brazil, China etc., lowering their estimates of mean uni-g. From the perspective of statistical modeling, thus, I can think of 3 approaches:

1. Count of top N -- Per-person rate of top-N universities, where top N is a tuning parameter. Best modeled using count models. This avoids the selection bias from not observing the left tail at the cost of statistical uncertainty and model interpretability.

2. Mean uni-g -- Mean score of all observed universities from that country. Biased upwards for low human talent and large population size countries. Avoids the arbitrariness of the top N tuning parameter.

3. Max uni-g -- Single highest scoring university. Avoids both issues but has even more statistical uncertainty and may be affected by historical factors relating to concentration of talent inside countries. Many countries put almost all talent in capital region, others split it up more evenly, and the former is much better for this metric.

I don’t know which approach is best, so I tried all of them. The simplest is average uni-g by country vs. NIQ, we don’t need to adjust for population size, so it’s just a scatterplot:

There is bias in that large countries are overestimated. E.g. USA has 1000s of unmeasured, low quality but accredited universities, all of which would substantially lower the mean uni-g if we had seen them. The same is true for low NIQ counties because we only observe their top universities. This general approach has issues with defining what is included as a university, and the data includes somewhere between 62% and 10% of American universities depending on these definitions.

The next idea is just to look at the single best scoring university by country (max uni-g) predicted from population size and NIQ. Population size makes the distribution larger, so there is greater chance of seeing a far right tail value, and NIQ moves the distribution towards the right and makes it larger, substantially increasing the max value seen. Since we have to control for population size, we can use the partial residuals for the plot:

This gives a better model, with sensible signal also among the low to average NIQ countries. The top positive outliers with regards to NIQ are those that are 1) large, and or 2) attract top talent from other countries, USA, UK, Switzerland, Singapore, and Canada. 4 of 5 of these are Anglos, and we have issues with English-speaking world granting high prestige to internationally known universities. Everybody knows Harvard etc. because they are commonly featured in American movies. Alternatively, maybe the modeling of the effect of population size is not quite right. After all, no one really thinks that log (population size) is the exactly right mathematical specification for how population size affects the likely right tail value.

Finally, the count models. I’ve chosen to stick with the top 200 N threshold, though one can tune/hack this parameter to get slightly better fit. There is a choice of what count model to use, ranging from the classic Poisson to negative binomial to 2-step hurdle-like models. Fortunately, the data does not suggest excess number of 0’s, so we can stick with the negative binomial. The issue here for the blogpost is that it doesn’t really give us a nice plot to show the model, only 30 out of ~200 countries have any top 200 university, so almost all countries just have a 0 observed rate. The most visual approach I can think of is using the empirical Bayes adjusted rates per million, which since they are directly adjusted for population size, can be shown with a simple scatterplot:

The grey values are the imputed values, that is, what the model expects the rate to be even though 0 was observed.

Overall, then, it is not entirely clear which approach is best for modeling this, but no matter the chosen approach, NIQs clearly predict university quality and quantity. One can go into models that control for confounders, spatial autocorrelation, or controlling for mediators like income/wealth, however, I am short on time, so this is it for today. Well, except for paying subscribers, who also get a fully searchable and downloadable dataset, so they can look up any university in database.

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The main analytic leverage for guessing at causality here is that countries changed status for the putative causal variables, and this is easy to measure. That is, the single market started with the European Economic Community in 1957 (Treaty of Rome), the initial customs union (Belgium, France, Italy, Luxembourg, the Netherlands and West Germany). It then gradually expanded over time to include more countries and more internal free trade. Thus, we can use the same country’s data from before and after they entered this union. Similarly, for the Eurozone, we can use the year they joined the Euro and adopted the currency. Thus, we don’t need to worry about between country differences so much because we are using within country variation and with year fixed effects. These are the dates for joining the two systems:

The dataset includes only countries that could plausibly join the European Union, so only European ones, including the ones that so far haven’t joined. These don’t affect the models much since they don’t have any within country variation to use to estimate the main predictor, but are shown here for completion’s sake.

The outcome variable is typically some kind of measure of economic growth. Typically GDP/cap is used, but it has severe issues for the European countries due to the tax haven problems (Ireland) and EU bureaucrats, lobbyists, and employees (Luxembourg), as covered in the prior post on economic growth as function of national IQ and poverty since 2000. The alternatives to GDP/person are GNI/person (foreign workers’ production is counted in their home countries, not their resident countries), and consumption/person (actual spending/person). The GDP/person time series covers more years, but at the cost of being ambiguous. Thus, a typical trade-off between measurement quality and data coverage. My preferred metric, median income, had too few years of coverage to be useful here, which was also true for GNI/person, so we were left with only consumption/person as a more clean metric.

Concerning the data source, for the oldest running time series, we have to use the Maddison database, and for later data we can use PWT‘s. These providers don’t provide the same metrics, so this choice also affects the metric used (GDP/consumption).

A number of other choices presented themselves. For instance, we saw before that being initially poor predicts faster growth, in particular if the IQ is relatively high for the current economic performance. This is a typical catch-up effect, also seen with children who have been out of school for a while. Since we are using fixed effects for countries, any stable characteristic is already controlled for, so there is no need (or possibility) of including the presumed stable NIQs (one could use varying PISA scores but coverage is not great and neither is the meaning of the changes clear). But we can still include a control for current economic performance (for that country x year). I decided to try 3 options: 1) no control, 2) last year’s economic performance, 3) last year’s relative economic performance (1 = average of countries that year).

Since the answers to which combinations of metrics, years, data sources, outlier handling etc. were not obvious, I ran a multiverse/specification curve model with these researcher degrees of freedom:

1. Data + metric: PWT+GDP, PWT+consumption, Maddison-GDP

2. Time: full (1950-present), 1991-present

3. Prior performance: none, lag(econ perf), lag(relative econ perf)

4. Outliers: none, trimmed

5. Greece: include, exclude

6. Estimator: double FE, Sun-Abraham (heterogeneity robust)

7. Single market coding: accession year, max(accession year, 1993), 1968 (Treaty of Rome in full effect)

8. Brexit: UK out in 2021, or still in

9. Croatia: included, excluded (it has only 2 years of data after joining the Eurozone, confounded with post-COVID lockdown recovery)

These choices result in 100s of models for both of the putative causal variables (single market, Eurozone), but fortunately, we can fit all of them quickly:

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Tackling first the matter of political leaning. There are some websites and academics sources that have published occupation level results for political leanings, mainly based on political donations. The most extensive I could find was Verdant Labs results from 2016 with results for 549 occupations. This is actually more than those in my ACS list (311), and Claude was able to match up 515 of them to the ACS occupation codes (OCCP). Here’s the most extremely skewed political occupations:

AI wrote 2008-2014 on the image, but actually it was just guessing. The website doesn’t appear to be updated since 2016, so the data are from around that time. This is somewhat before the Republican change into the populist party, so it is possible that some occupations have moved substantially since then. However, for our fertility estimates, the time is sensible because the fertility data is from 2013-2022. To note about these data based on donations is that they reflect people who actually donate money to politicians, which are those who are more invested in politics, and richer. This demographic skews Democrat in modern USA. There may also be issues with shy Republicans who don’t donate publicly (out of fear of reprisals), or just don’t donate at all (surveys show Democrat voters are more interested in politics in general). At least, there seems to be a dearth of activist class jobs with ~100% Republican donations emerging. Every single occupation in the top Democrat list is more skewed towards Democrats than the most Republican occupation is towards Republicans (10% Democrat for Miners vs. 1-9% Republican in all top 25 for Democrats). This is also why many occupations aren’t seen at all despite being large. There are 600k American women working with hand packing things, but they don’t donate a lot of money to politicians, so their leaning cannot be estimated this way.

One of the lowest female fertility occupations was in fact librarian (various subtypes), which we see is in the top list for most left-wing occupations. Using the matching overlap of occupations we get this simple result:

The correlation is a bit better than the other ones we tried, r = -0.23.

Regarding the modeling, there are some thorny questions about measurement/sampling error and representativeness:

• The fertility rates are estimates, with some error bars. If these were measured better, the model itself would fit better. Thus, our results are underestimates compared to the hypothetical situation where we sampled an infinite number of women in each occupation.

• The simplest way to counteract this bias is to use precision weights, that is, 1/standard error. However, because precision is directly a function of the sample size and the sample size is a function of the size of the occupations, weighing by precision also weighs results towards the larger occupations. This thus changes what is being modeled from being “the universe of all jobs” to “the universe of jobs relative to their size”.

• Alternatively, one can use the cool SIMEX method, which should produce about the same results.

• By joining more variables to the dataset, we are losing some occupations that couldn’t be mapped confidently. This thus represents another subset of the number of occupations which itself can affect the results aside from the introduction of another predictor.

With these caveats in mind, here are some model results:

I’ve tried every modeling approach I could think of, which are:

• OLS, no weights. This is the cookie cutter and identical to the method used before.

• WLS, weighted. This weighs each occupation by the precision with which we have measured its fertility (the outcome variable), and thus its size in the workforce.

• FGLS, also weighted, but less so. This is a poor man’s alternative to the multi-level model. The difference being that we add a constant to the denominator to prevent large occupations from having almost all the weight. This is akin to random effects meta-analysis.

• HLM, also weighted but using a multi-level model that uses the fact that the occupations are part of 25 clusters to stabilize the results (23 with data post merge).

• SIMEX, which uses simulated extra errors to the variables to try to back-estimate the effects of the variables at SE=0. The clever thing about this is that it can use cell-level error estimates in any variable, and thus we can also account for the estimation error in the political leaning variable (100 total donors for occupation X and 90% gave to Democrats vs. 10000 total donors for occupation Y and 90% gave to Democrats, these estimates are not equally precise, the former may be quite wrong but the latter is not likely to be).

Looking across the models, we see at least some consistency. All models find that female% of occupations predict higher fertility with about the same effect size around 0.25. The relatively unweighted models find large negative effects of Democrat% support, but these are smaller or not above chance levels in the weighted models. I think this is because the high Democrat% occupations are numerically small and thus imprecise and thus have small importance when using weights. Artistic jobs predict lower fertility with fairly stable slopes around -0.30, but varying p values. These models have only 143 cases because many occupations could not be matched with the OCCP codes or the ones with political donation data, and with weights, the effective sample size is much smaller and thus the results will become unstable.

Regarding the male results, it is tricky. There is a variable for cohabiting opposite sex partner, which is then the father presumably. Any non-cohabiting father is not counted this way. There is another method which is the count of resident children below the age of 1, but this would presumably give about the same result. With this in mind, here are the results across sex:

The correlation is not very strong 0.30. However, this is downwards biased by both the estimation errors for women and the even larger ones for men. The doubly adjusted correlation is 0.45, about 50% larger, based on reliabilities of 0.78 for women and 0.67 for men. Interestingly, the cross-wave stability for both sexes was 0.74 corrected for reliability, so the temporal changes seem to be happening at the same speed in both sexes (between the 2013-2017 and 2018-2022 datasets). Here’s the top and bottom male occupations:

Funny that even men in nurse-like roles are high fertility. And for good measure, here are the same models fit on the male data:

Note that Democrat% predicts negatively also for men regardless of the model, while female% does not reliably predict, though it is p<5% in 2 models. Conventional and artistic also show up as negative predictors, the same as for women. These models with politics added did not have sufficient precision to estimate the nonlinear effects of complexity, or at least, it was not detectable with this reduced sample and extra covariates.

Overall, the differences in fertility across occupations are generally explainable in sensible terms for both men and women, and largely due to the same factors. Of course, we cannot be confident about causality with these cross-sectional results, but the results do point in some directions of interest.

These are just the top and bottom 25 occupations. There are some questions about the causation. The most obvious interpretation is that some jobs are easier to combine with family making than others, so this would represent a causal effect from occupation to fertility. The second most obvious interpretation is that women who want to make families don’t choose their occupations at random, but choose those that are compatible with family life or otherwise preferred by (would be) mothers, and that’s why some occupations are higher in fertility. The third interpretation is that having children caused women to move into specific occupations afterwards, thus violating the stability assumption. This third option is most likely the case for telemarketer, which is presumably something women decide to do to make some money while staying at home with young children (a good working from home/remote job). However, for many other jobs, changing jobs is not so easy. Working as a nurse or physician (both in top 25) requires a long-ish degree and passing some test, so it is not so easy to just decide to change to that job tomorrow. Regarding family life compatibility, the interpretation is not so obvious for some jobs. In the low fertility group, we see flight attendants, which makes a lot of sense. They keep traveling around and pregnancy while working in mid-air sounds unwise (in fact, often prohibited). On the other hand, web development is easy to combine with family formation, but they are among the least fertile women. In the high fertility group, we see a lot of healthcare jobs, which I guess may have flexible hours, but also many are physical labor intensive (butcher, packaging, machine filling, agricultural workers) that don’t sound like they would make for good jobs compatible with motherhood. Overall, it doesn’t immediately seem that between job fertility rates are caused by the jobs themselves but rather must mainly be due to self-selection of preexisting differences among the women who choose them.

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• Van Pelt, D., & Kirkegaard, E. O. (2026). Big Data, Deep Roots: Correlating Surname Genetic Ancestry and Socioeconomic Status across Millions of Americans. Comparative Sociology, 25(2), 239-280. https://doi.org/10.1163/15691330-bja10162

Genetic variation plays a significant role in shaping socioeconomic status. Conventional census racial categories (Black, White, Asian, Hispanic) obscure substantial variation among ancestry groups. Surnames reflect ancestral lineage and genetic heritage, enabling finer measurement. The authors combined 23andMe genetic ancestry data on surnames with surnames yielded from government financial records, criminal databases, Wikipedia entries, and physician licensure records. They found that genetic ancestry strongly predicted surname-level outcomes across all metrics, with substantial differences in social standing among ethnic groups. Ashkenazi Jews and Indians ranked highest; British/Irish and Iberian ranked lowest among Europeans; highly selected immigrant groups such as Arabs and Iranians scored above Europeans.

Ancestry-related social gaps are much researched in the USA. Most of the research focuses on the relatively crude racial categories of Black, White, Hispanic, Asian. But there is also some research on the more fine-grained differences. The origin of the study was that some people posted 23andme’s surname page on X. You can look up almost any surname found in the American population there to see statistics about it, including ancestry results from 23andme customers. For instance, looking up “Brown”, we can see that the mean ancestry for this group of customers is:

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