. 2021 Mar 18;11(6):jkab057. doi: 10.1093/g3journal/jkab057

Table 2.

Scenarios and covariance matrices for testing the gene-environment interaction effect

Scenario	Model	Study design	Σ_y	Σ_v
Unrelated	LR	Unrelated	$σ_{r}^{2} I$	diag(D)
Families	LMM	Related	$σ_{a}^{2} K + σ_{a i}^{2} K_{I} + σ_{r}^{2} I$	$K_{D} = D ° K$
Unrelated+ Grouping	LMM	Unrelated	$σ_{f}^{2} F + σ_{r}^{2} I$	diag(D)
Unrelated+ GRM	LMM	Unrelated	$σ_{g}^{2} G + σ_{g i}^{2} G_{I} + σ_{r}^{2} I$	diag(D)

The relationship matrices specific to testing gene-environment interactions are as follows: K_I is an interaction kinship matrix (Sul et al. 2016); G_I is an interaction genetic relationship (GRM) matrix defined similarly to K_I.