Algorithm 2 A fast operational scheme of Algorithm 1.

1.Step 2.1 of Algorithm 1 is performed by running the linear mixed model with our initial fixed $\mathit{\gamma }$ from Step 1.2 of Algorithm 1 to obtained updated values of ${\lambda }_1$, $\mathit{\beta }$, and $\mathit{\alpha }$. 2.Step 2.2 is performed with solving the group regularity problem (8) through the Gauss–Newton algorithm using cross-validation-based tuning (e.g., R package oem). 3.Rerun Step 2.1 using the updated $\mathit{\gamma }$ from Step 2.2 to obtain the estimates for $\mathit{\beta }$ and $\mathit{\alpha }$.