Figure 1.

An illustration for the computation of the design matrix for the random effects {r_l; l = 1, …, p} in Model 1. This gene set has 3 genes (variables) and the dataset has 12 samples (observations). Covariance Matrix = estimated gene-gene covariance matrix ∑̂. Under “Eigenvectors”, Prin 1 = the estimated first eigenvector α̂₁ of ∑̂, and λ̂₁ = 0.09802458 is the estimated first eigenvalue of ∑̂. The column in design matrix corresponding to r₁ is then $\sqrt{0.098}{\widehat{\alpha }}_1$, note that they vary according to genes, so the random effects have sub-index i in Model 1.