Sunde, H. F.; Eilertsen, E. M.; Torvik, F. A.

Partners tend to have similar levels of education. Previous studies indicate that this is likely due to some form of indirect assortative mating but there is not a consistent understanding of this process. Understanding indirect assortment is crucial for correctly adjusting for assortative mating, and for understanding intergenerational transmission. We attribute previous inconsistencies to idiosyncratic models and inconsistent use of relevant terms. In this paper, we develop a new framework for understanding indirect assortative mating and provide updated definitions of key terms. We then develop a model (the iAM-ACE-model) that can use partners of twins and siblings to distinguish the degree of assortment on genetic, social, and individual characteristics. We also expand this model to include children of twins and siblings (the iAM-COTS model), allowing us to explain parent-offspring similarity while accounting for indirect assortative mating and geneenvironment correlations. We apply the models on educational attainment using 1,529,144 individuals in 209,792 extended families from Norwegian registry data and the Norwegian Twin Registry. The analysis suggests that partners correlate .67 (95% CIs: .66, .70) on a latent sorting factor associated with educational attainment, which we estimate to be about 30% (26%, 35%) heritable, 42% (37%, 47%) sibling-shared environment, 8% (4%, 13%) twin-shared environment, 17% (16%, 19%) gene-environment correlations, and 3% (2%, 5%) non-shared environment. The implied genotypic correlation between partners (r = .33) is comparable to earlier studies, and higher than expected under direct assortment. Most of the parent-offspring correlation (r = .33) was attributable to passive genetic transmission (62%), with the rest attributable to passive environmental transmission (23%) and direct phenotypic transmission (15%). Environmental transmission was estimated lower in alternative models that assumed direct assortment, but these did not fit the data well.