Correction to: Behavior Genetics (2021) 51:45–57 https://doi.org/10.1007/s10519-020-10027-7

In the article “The Moderating Influence of School Achievement on Intelligence in Young Adulthood” by Emilie R. Hegelund, Erik L. Mortensen, Trine Flensborg-Madsen, Jesper Dammeyer, Kaare Christensen, and Wendy Johnson (Behavior Genetics, Vol. 51, No. 1, pp. 45–57. https://doi.org/10.1007/s10519-020-10027-7), we estimated the gene-environment interaction model referred to as the ‘full moderation model’ using the umxGxEbiv function from the umx package (version 3.0.5; Bates et al. 2019) in R.

Since the publication of our article, Prof Timothy Bates, the developer of the umxGxEbiv function, has discovered that the function produced incorrect expected covariance matrices because it reversed the moderator and outcome variables at one point in the script (personal correspondence with Prof Timothy Bates, 7 July 2021; Bates 2021). Rerunning our statistical analyses using the OpenMx package (version 2.19.5) in R led to differences from the full moderation model results, presented in Table 2 and Fig. 3 in the Results section as well as in Tables 4 and 5 in the Appendix of our above paper. The corrected tables and figures are presented below.

Table 2 Parameter estimates from the best-fitting full moderation model and derived variance components and genetic and environmental correlations
Full size table
Fig. 3
figure 3

Variance in IQ scores as a function of grade point average (GPA) in lower secondary school, by source of variance. Note A refers to genetic variance, C to shared environmental variance, and E to non-shared environmental variance. The dotted line shows the empirical variance.

Full size image
Table 4 Parameter estimates from the full moderation model with all moderation paths fixed to 0 (Cholesky model)
Full size table
Table 5 Fit statistics from the full moderation models of variance components
Full size table

As can be seen, the best-fitting version of the full moderation model investigating the extent to which grade point average (GPA) in lower secondary school moderated the genetic and environmental influences on IQ scores suggested only moderation of the common genetic influences. More specifically, the model suggested that the genetic variance in IQ scores was greater among individuals with low GPAs (Table 2 and Fig. 3). The genetic variance was 0.74 among individuals with a GPA of one standard deviation below the mean, 0.62 among individuals with an average GPA, and 0.52 among individuals with a GPA of one standard deviation above the mean. The shared environmental variance and the non-shared environmental variance were constant across the range of GPA (0.06 and 0.20, respectively).

Though the corrected full moderation model fit the empirical data much better than the full moderation model estimated using the umxGxEbiv function from the umx package (version 3.0.5), the published article’s central message still holds. That message is that neither of the applied models generated results that described the data well, and this is very common when the two variables are highly correlated, especially when reciprocally so. We need better statistical models of gene-environment interplay because this kind of situation is common for many important developmental characteristics related to health and wellbeing and of much interest to behaviour genetics researchers. In particular, such models need to be able to distinguish uniform main effects from moderated covariance.