The multilevel approach  is inspired by the mixed-model framework and uses a split-up variation of the (n T)×p matrix X that contains the observations of p variables (clinical biology variables or gene expressions) on n animals with T=4 times of measurements: 4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ {\begin{aligned} X = \underbrace{X_{..}}_{\textrm{offset term}} + \underbrace{X_{b}}_{\textrm{between-animal deviation}} + \underbrace{X_{w}}_{\textrm{within-animal deviation}} \end{aligned}} $$ \end{document}X=X..⏟offset term+Xb⏟between-animal deviation+Xw⏟within-animal deviation