There are three random-effect terms that include modality: $[\tau R\alpha ]ijt$, $[\tau C\alpha ]ikt$, and $[\tau RC\alpha ]ijkt$. They correspond to 12 variance components: $\sigma AR02,\sigma AC02,\sigma ARC02$ are for modality A, nondiseased cases $(i=A;t=0)$, $\sigma AR12,\sigma AC12,\sigma ARC12$ are for modality A, diseased cases $(i=A;t=1)$, $\sigma BR02,\sigma BC02,\sigma BRC02$ are for modality B, nondiseased cases $(i=B;t=0)$, and $\sigma BR12,\sigma BC12,\sigma BRC12$ are for modality B, diseased cases $(i=B;t=1)$. The sums of the variance components that are specific to modality A and B are Display Formula
$\sigma A2=\sigma AR02+\sigma AC02+\sigma ARC02+\sigma AR12+\sigma AC12+\sigma ARC12,$(4)
Display Formula$\sigma B2=\sigma BR02+\sigma BC02+\sigma BRC02+\sigma BR12+\sigma BC12+\sigma BRC12.$(5)