Non-Shared Environment Doesn’t Just Mean Schools And Peers

Scott Alexander has a new post out summarizing the interpretations of what constitutes non-shared environment in the ACE model estimates from standard (MZ-DZ) twin studies. I’m happy that he wrote that up because I had been thinking of writing up the same points, but he is a better writer than I am. Still, his post is a bit short on numbers and supporting research, so I will attempt to address that by presenting some supporting data in this post.

Theory

When we test persons on more than one test, we consistently find that, statistically, someone who does better at one test, also does better at every other test. In other words, all the tests are positively correlated (the positive manifold). If one has a genetically informative sample (and one should!), one can break down the correlations between tests into the part that is A, C and E (cholesky decomposition). Let’s make some predictions from causal models before looking at studies:

  1. If E is entirely measurement error, then one would expect E correlations of ~0 between tests. Specifically, the correlations should have a mean of 0 and be normally distributed. In general, on the measurement error model, E-caused variation in a trait should have no relationship to other variables, no matter which variables. Error, by definition, cannot be correlated with anything aside from chance. (If in an analysis errors are somehow correlated, one must take this into account.)
  2. If E is entirely specific causes, one would expect to see the same results as in (1). Specific causes are things like plain luck in guessing (measurement error). This would cause higher scores on one test, but not on another.
  3. If E is entirely general causes, one should expect to see strong positive correlations between tests. This could be things like having a teacher or friend of the family that inspires one to perform well in school. If tests were taken on the same day or in close proximity, it could also be transient health effects.
  4. If E is some kind of mix of measurement error, specific causes and general causes, one would expect to see weak but positive correlations between tests.

Note I have split causes into specific (affects only one outcome) and general (affects all outcomes), but that this is a simplification. It is possible that some causes affect e.g. outcomes A+B, but not C+D, while other causes affect A+C but not B+D, and so on. Such group factor-like causes will also cause positive correlations between E-caused variances, but not strong correlations.

Data – Cognitive ability and scholastic tests in the UK

Rimfeld, K., Kovas, Y., Dale, P. S., & Plomin, R. (2015). Pleiotropy across academic subjects at the end of compulsory education. Scientific reports, 5.

Abstract. Research has shown that genes play an important role in educational achievement. A key question is the extent to which the same genes affect different academic subjects before and after controlling for general intelligence. The present study investigated genetic and environmental influences on, and links between, the various subjects of the age-16 UK-wide standardized GCSE (General Certificate of Secondary Education) examination results for 12,632 twins. Using the twin method that compares identical and non-identical twins, we found that all GCSE subjects were substantially heritable, and that various academic subjects correlated substantially both phenotypically and genetically, even after controlling for intelligence. Further evidence for pleiotropy in academic achievement was found using a method based directly on DNA from unrelated individuals. We conclude that performance differences for all subjects are highly heritable at the end of compulsory education and that many of the same genes affect different subjects independent of intelligence.

Table 2 has the correlations we want. I took the liberty of renaming E to be what it really is: Everything else (anything not genetic or common between same-aged siblings).

Test Intelligence English Mathematics Science Humanities Second language Art Business informatics
Phenotypic
Intelligence 1
English 0.52 (0.50–0.54) 1
Mathematics 0.56 (0.53–0.58) 0.69 (0.69–0.70) 1
Science 0.48 (0.46–0.51) 0.66 (0.65–0.67) 0.71 (0.70–0.72) 1
Humanities 0.48 (0.45–0.50) 0.77 (0.76–0.78) 0.69 (0.68–0.70) 0.67 (0.66–0.69) 1
Second language 0.48 (0.45–0.51) 0.71 (0.70–0.73) 0.67 (0.65–0.68) 0.63 (0.62–0.65) 0.68 (0.66–0.69) 1
Art 0.36 (0.33–0.39) 0.57 (0.55–0.59) 0.50 (0.48–0.52) 0.49 (0.46–0.51) 0.57 (0.55–0.59) 0.53 (0.50–0.55) 1
Business informatics 0.44 (0.40–0.47) 0.62 (0.60–0.63) 0.63 (0.61–0.64) 0.58 (0.56–0.60) 0.62 (0.60–0.63) 0.57 (0.55–0.60) 0.49 (0.46–0.51) 1
 
A – (Additive) Genotypic
Intelligence 1
English 0.65 (0.57–0.75) 1
Mathematics 0.69 (0.62–0.76) 0.73 (0.70–0.75) 1
Science 0.61 (0.51–0.73) 0.73 (0.69–0.78) 0.78 (0.75–0.82) 1
Humanities 0.58 (0.48–0.69) 0.88 (0.84–0.92) 0.74 (0.71–0.78) 0.75 (0.70–0.80) 1
Second language 0.59 (0.49–0.71) 0.83 (0.78–0.88) 0.72 (0.71–0.76) 0.68 (0.62–0.74) 0.76 (0.70–0.83) 1
Art 0.44 (0.31–0.60) 0.65 (0.58–0.73) 0.56 (0.49–0.64) 0.51 (0.49–0.61) 0.62 (0.54–0.71) 0.56 (0.48–0.67) 1
Business informatics 0.56 (0.44–0.72) 0.72 (0.64–0.81) 0.70 (0.63–0.77) 0.70 (0.60–0.80) 0.69 (0.61–0.78) 0.64 (0.54–0.75) 0.59 (0.43–0.75) 1
 
C – Common environment
Intelligence 1
English 0.79 (0.41–0.82) 1
Mathematics 0.88 (0.51–1.00) 0.98 (0.93–1.00) 1
Science 0.85 (0.41–1.00) 0.84 (0.74–0.93) 0.91 (0.84–0.91) 1
Humanities 0.94 (0.54–0.94) 0.91 (0.84–0.97) 0.95 (0.90–1.00) 0.90 (0.80–0.98) 1
Second language 0.93 (0.46–1.00) 0.83 (0.71–0.93) 0.88 (0.77–0.88) 0.89 (0.77–0.89) 0.90 (0.78–0.97) 1
Art 0.82 (0.25–1.00) 0.81 (0.63–0.88) 0.83 (0.62–1.00) 0.87 (0.65–1.00) 0.91 (0.73–1.00) 0.91 (0.70–1.00) 1
Business informatics 0.94 (0.40–1.00) 0.79 (0.79–0.96) 0.86 (0.71–0.90) 0.71 (0.54–0.71) 0.89 (0.73–1.00) 0.79 (0.58–0.96) 0.66 (0.35–0.98) 1
 
E – Everything else
Intelligence 1
English 0.19 (0.12–0.25) 1
Mathematics 0.21 (0.19–0.27) 0.26 (0.22–0.30) 1
Science 0.16 (0.08–0.23) 0.27 (0.23–0.31) 0.32 (0.28–0.36) 1
Humanities 0.17 (0.09–0.24) 0.35 (0.31–0.39) 0.29 (0.25–0.33) 0.28 (0.23–0.32) 1
Second language 0.15 (0.06–0.18) 0.23 (0.18–0.28) 0.31 (0.25–0.36) 0.26 (0.20–0.31) 0.22 (0.16–0.27) 1
Art 0.10 (0.01–0.20) 0.18 (0.12–0.24) 0.10 (0.10–0.16) 0.14 (0.14–0.20) 0.20 (0.13–0.27) 0.12 (0.04–0.20) 1
Business informatics 0.09 (–0.01–0.19) 0.21 (0.14–0.26) 0.27 (0.21–0.33) 0.23 (0.16–0.26) 0.23 (0.21–0.29) 0.24 (0.15–0.33) 0.17 (0.06–0.28) 1

 

It is not easy to get the general pattern of results when the data are presented like that, so let’s visualize the correlations in a better way.

GCSE_intercors_1

 

 

 

 

 

 

Observations:

  • All types of correlations were uniformly positive (‘extended positive manifold’).
  • There are large average differences between the distributions:
    • The C effects are very strongly correlated (mean = .86), so whatever the C causes are, they are very general.
    • The A effects are also very strong (mean = .67). This is what the researchers consider to be the main finding, namely that it appears that there are some genes that affect multiple of the 7 scholastic tests and the cognitive ability measure. One cannot conclude that there are genes that affect them all from this data, a sampling + multiple group factors model would give the same/similar results.
    • The E effects are not strong (mean =.21). Whatever E is, it is mostly specific causes.

Data – Cognitive ability, scholastic achievement and predictors in the UK

Using the same dataset, researchers have used the same method to examine correlations between cognitive ability, scholastic achievement (mean of GCSE tests) and various other predictors: self-efficacy, school environment, home environment, personality, well-being, parent-reported behavioral problems, child-reported behavioral problems, and health.

Krapohl, E., Rimfeld, K., Shakeshaft, N. G., Trzaskowski, M., McMillan, A., Pingault, J. B., … & Plomin, R. (2014). The high heritability of educational achievement reflects many genetically influenced traits, not just intelligence. Proceedings of the National Academy of Sciences, 111(42), 15273-15278.

The supplementary materials have the data we want (Table S4, S8, S9 and S10). We have to work a bit since they are only supplied in PDF format (which kind of journal allows or even forces researchers to share data in a near-useless format?). I used Abbyy FineReader to get the data out.

The raw results broken down by ACE and observed (Phenotypic):

P GCSE Intelligence Self-efficacy School environment Home environment Personality Well-being Parent-reported behavior problems Child-reported behavior problems Health
GCSE 1
Intelligence 0.58 (0.56-0.60) 1
Self-efficacy 0.49 (0.46-0.51) 0.35 (0.33-0.38) 1
School environment 0.34 (0.32-0.37) 0.24 (0.21-0.27) 0.46 (0.43-0.48) 1
Home environment 0.17 (0.14-0.20) 0.13 (0.10-0.16) 0.30 (0.28-0.33) 0.52 (0.50-0.55) 1
Personality 0.28 (0.25-0.31) 0.18 (0.15-0.21) 0.42 (0.39-0.45) 0.39 (0.37-0.42) 0.38 (0.36-0.41) 1
Well-being 0.26 (0.23-0.28) 0.17 (0.14-0.20) 0.41 (0.38-0.44) 0.54 (0.52-0.56) 0.61 (0.59-0.63) 0.51 (0.49-0.54) 1
Parent-reported behavior problems 0.33 (0.31-0.35) 0.26 (0.22-0.29) 0.26 (0.22-0.29) 0.29 (0.26-0.33) 0.31 (0.27-0.35) 0.22 (0.18-0.26) 0.38 (0.35-0.41) 1
Child-reported behavior problems 0.25 (0.23-0.27) 0.18 (0.15-0.21) 0.36 (0.33-0.38) 0.39 (0.37-0.42) 0.42 (0.39-0.45) 0.30 (0.27-0.33) 0.54 (0.52-0.56) 0.38 (0.36-0.40) 1
Health 0.08 (0.05-0.12) 0.07 (0.03-0.11) 0.14 (0.10-0.18) 0.23 (0.20-0.27) 0.26 (0.23-0.30) 0.08 (0.04-0.12) 0.32 (0.28-0.35) 0.17 (0.15-0.20) 0.42 (0.40-0.44) 1
A GCSE Intelligence Self-efficacy School environment Home environment Personality Well-being Parent-reported behavior problems Child-reported behavior problems Health
GCSE 1
Intelligence 0.76 (0.68-0.84) 1
Self-efficacy 0.62 (0.52-0.73) 0.64 (0.49-0.81) 1
School environment 0.43 (0.30-0.60) 0.40 (0.22-0.61) 0.62 (0.43-0.81) 1
Home environment 0.10 (-0.02-0.21) 0.08 (-0.09-0.23) 0.25 (0.06-0.41) 0.53 (0.35-0.69) 1
Personality 0.47 (0.35-0.61) 0.29 (0.15-0.43) 0.58 (0.42-0.72) 0.63 (0.46-0.82) 0.55 (0.41-0.69) 1
Well-being 0.29 (0.17-0.42) 0.24 (0.07-0.41) 0.47 (0.29-0.65) 0.65 (0.49-0.83) 0.78 (0.66-0.89) 0.68 (0.55-0.83) 1
Parent-reported behavior problems 0.46 (0.40-0.51) 0.36 (0.24-0.48) 0.43 (0.30-0.56) 0.44 (0.27-0.63) 0.35 (0.22-0.49) 0.30 (0.16-0.45) 0.35 (0.23-0.48) 1
Child-reported behavior problems 0.39 (0.30-0.48) 0.25 (0.11-0.39) 0.57 (0.43-0.75) 0.70 (0.55-0.93) 0.55 (0.43-0.67) 0.45 (0.32-0.58) 0.74 (0.63-0.84) 0.45 (0.38-0.53) 1
Health 0.09 (-0.01-0.19) 0.09 (-0.08-0.29) 0.13 (-0.09-0.36) 0.28 (0.01-0.56) 0.25 (0.06-0.46) 0.12 (-0.07-0.35) 0.38 (0.19-0.59) 0.15 (0.06-0.23) 0.54 (0.44-0.66) 1
C GCSE Intelligence Self-efficacy School environment Home environment Personality Well-being Parent-reported behavior problems Child-reported behavior problems Health
GCSE 1
Intelligence 0.65 (0.40-0.87) 1
Self-efficacy 0.47 (0.28-0.65) -0.09 (-0.48-0.27) 1
School environment 0.62 (0.32-0.98) 0.28 (-0.27-0.80) 0.55 (0.19-0.89) 1
Home environment 0.66 (0.34-0.92) 0.49 (-0.04-0.86) 0.66 (0.31-0.90) 0.85 (0.39-1.00) 1
Personality -0.03 (0.94-0.86) 0.09 (-0.97-0.91) 0.48 (-0.76-0.99) 0.48 (-0.81-0.99) 0.67 (-0.58-1.00) 1
Well-being 0.46 (0.18-0.72) 0.13 (-0.31-0.63) 0.40 (0.05-0.67) 0.81 (0.39-0.98) 0.75 (0.40-0.95) 0.49 (-0.56-1.00) 1
Parent-reported behavior problems 0.16 (0.04-0.27) 0.25 (-0.05-0.54) 0.09 (-0.13-0.28) 0.41 (0.12-0.76) 0.57 (0.28-0.82) 0.61 (-0.19-1.00) 0.79 (0.56-0.96) 1
Child-reported behavior problems 0.19 (-0.18-0.54) 0.12 (-0.45-0.68) 0.52 (0.01-0.81) 0.63 (-0.04-0.95) 0.83 (0.42-0.98) 0.81 (-0.26-1.00) 0.80 (0.41-0.98) 0.80 (0.52-0.99) 1
Health 0.17 (-0.09-0.45) 0.32 (-0.26-0.81) 0.45 (0.01-0.86) 0.43 (-0.28-0.91) 0.74 (0.13-0.98) 0.65 (-0.57-1.00) 0.33 (-0.16-0.76) 0.38 (0.20-0.62) 0.77 (0.25-0.98) 1
E GCSE Intelligence Self-efficacy School environment Home environment Personality Well-being Parent-reported behavior problems Child-reported behavior problems Health
GCSE 1
Intelligence 0.24 (0.17-0.31) 1
Self-efficacy 0.31 (0.24-0.37) 0.21 (0.15-0.28) 1
School environment 0.13 (0.07-0.20) 0.09 (0.03-0.16) 0.31 (0.25-0.36) 1
Home environment 0.05 (-0.02-0.13) 0.10 (0.03-0.17) 0.23 (0.17-0.30) 0.45 (0.40-0.50) 1
Personality 0.14 (0.06-0.21) 0.08 (0.20-0.15) 0.33 (0.27-0.39) 0.24 (0.18-0.30) 0.23 (0.16-0.29) 1
Well-being 0.10 (0.03-0.17) 0.12 (0.05-0.18) 0.36 (0.30-0.42) 0.39 (0.33-0.44) 0.43 (0.37-0.48) 0.41 (0.35-0.46) 1
Parent-reported behavior problems 0.20 (0.15-0.25) 0.12 (0.04-0.20) 0.20 (0.12-0.28) 0.09 (0.02-0.17) 0.13 (0.05-0.22) 0.09 (0.01-0.17) 0.19 (0.11-0.26) 1
Child-reported behavior problems 0.12 (0.06-0.17) 0.13 (0.06-0.20) 0.16 (0.09-0.22) 0.15 (0.09-0.22) 0.26 (0.19-0.32) 0.15 (0.06-0.24) 0.35 (0.30-0.41) 0.27 (0.22-0.31) 1
Health 0.00 (-0.06-0.06) -0.04 (-0.13-0.05) 0.02 (-0.08-0.11) 0.14 (0.05-0.23) 0.15 (0.06-0.24) -0.02 (-0.11-0.07) 0.25 (0.17-0.33) 0.07 (0.02-0.12) 0.27 (0.22-0.31) 1

 

But as before, they are hard to grasp in that format. So we group the numbers by ACE with P for comparison, and plot.

 

GCSE_intercors_2

 

Observations:

  • Large overlap between distributions, but nevertheless clear differences between distributions:
    • The P distribution is fairly normal (skew = .15) but weak to moderate in size (mean = .32).
    • The C distribution is again the strongest (mean = .48), but it is very flat and has a long left tail (min = -.09, skew = -.41).
    • The A distribution nearly as strong as C (mean = .42), is more symmetric (skew = -.06) and but still flatish.
    • The E distribution is weak (mean =.19) but fairly pointy and somewhat skewed to the right (skew = .36). Whatever the causes of the E variation is, it is mostly but not entirely specific to each predictor. The largest values concern the relationships of well-being to other variables (mean = .29) as well as the relationship between school and home environment (.45). Health events seems to be the least likely explanation because this variable has the weakest relationships (mean = .09).

Data – Predictive power of AE vs. E variation in cognitive ability

Let’s look at another type of data. Sibling (FS, DZ) and twin (MZ) control studies are interesting because they by virtue of the research design control for C since they only examine within family variance in variables. See my prior post on sibling designs.

First, let’s consider a study that examined MZ differences in cognitive ability and outcome variables:

Nedelec, J. L., Schwartz, J. A., Connolly, E. J., & Beaver, K. M. (2012). Exploring the association between IQ and differential life outcomes: Results from a longitudinal sample of monozygotic twins. Temas em Psicologia, 20(1), 31-43.

The data is in Table 2.

MZ_diffs_table

We look at the B column (standardized betas) and note the general results: not much. One might be tempted to go for the near p<a finding for educational attainment, but it is offset by the even larger, negative finding for income. In fact, of 17 tested relationships, 1 had p<a with an unimpressive beta of -.185, which is about what one would expect based on chance (1/20).

It would appear that non-genetic non-common environment differences in cognitive ability do not predict outcomes very well, at least in the Add Health sample. To be fair, the IQ measure is not too good (“abridged version of the Peabody Picture Vocabulary Test- Revised (PPVT-R)”)and the sample size is not large (varies with available data but max N = 166 pairs).

In comparison, let’s consider a study of differences between ordinary full siblings in cognitive ability and outcomes:

Murray, C. (1998). Income inequality and IQ. AEI Press.

In the study, siblings growing up in two-parent families are compared on IQ (the same measure as used in The Bell Curve) and later outcome variables. Murray looks at many outcomes, but let’s make it simple and only include educational attainment, occupational prestige, income, and unemployment. I attach the tables below:

murray_sib_IQmurray_sib_edumurray_sib_occumurray_sib_workmurray_sib_income

The numbers above are given in natural units so that they are easier to understand if one is familiar with them. However, we also want the standardized units, so they are easier to compare across variables and studies. These are found in another table:

murray_sib_compare

So, we see clear effects when comparing siblings, but either no effects or effects too weak to be reliably detected in the study when comparing MZs. Again, to be fair, there were numerous other differences between these two studies and perhaps they explain some of the discrepancy in the results. It would be preferable if one could obtain a large public dataset of various family members including an oversampling of twins (who would otherwise be too few for useful analysis due to their rarity), and outcome variables, so that one could check whether MZ differences in traits matter. Recall, that the measurement error model predicts that these should have a mean of 0 and be normally distributed around 0. This is a strong prediction that can be tested.

General conclusion

The general causes model of E seems empirically untenable and measurement error cannot wholly account for the E variance. The UK studies found small but positive intercorrelations between E-variances, which is inconsistent with the measurement error model. The Add Health study found inconsistent results for IQ in MZ sample, as predicted by the measurement error model. The NLSY79 sibling analysis shows that AE-variance is clearly predictive in expected directions.

Code and data