The General Linear Model Sample Clauses

The General Linear Model. ‌ Suppose that there are 1 nMZ > 0 MZ twin pairs (nMZ individuals), 1 nDZ > 0 DZ 2 2 r twin pairs (nDZ individuals), and nS ≥ 0 singletons (unrelated subjects), and in total n = nMZ + nDZ + nS participants in the experiment. For a particular voxel r ∈ {1, . . . , K}, the column vector Y(k) is used to denote the observations from all these n participants for the phenotype k ∈ {1, . . . , J}: Y(k) = . Y(k) , Y(k) , . . . , r 1,1,r Y(k) 1 2,1,r , Y(k) 1 , . . . , nMZ+1, 2 nMZ+1,r Y (k) nMZ+nDZ+1,0,r nMZ+2, 2 nMZ+1,r , Y

The General Linear Model. ‌ Assume that there are J phenotypes (or J phenotypic elements for a high-dimensional phenotype) considered for the multivariate modeling. Suppose the sample contains totally n subjects, as stated in Section 3.1, including nMZ MZ twins ( 1 nMZ pairs), nDZ DZ twins ( 1 nDZ pairs) and nS singletons. In this chapter, we require an ad- ditional index k to account for the different phenotypes jointly modeled. For a particular voxel, the voxel-wise data vector for phenotype k is denoted as Y(k) (k = 1, . . . , J) by eliminating the voxel index r. We suppose the number of covari- ates included for the phenotype k is pk − 1. Generalizing the univariate GLM model (3.1) for a single phenotype with the data vector Y(k) to the multivariate case yields the multivariate GLM with respect to all these J phenotypes: Y(1)   X(1)β(1) + s(1)  .  .  =    .   ( .) Y(J) X(J)β J + s(J) X(1) · · · 0  β(1)  s(1)  = .