Mixed-Effects Model Structure

digraph mlm {
  rankdir=TB;
  graph [bgcolor=transparent];
  node [shape=box, style="rounded,filled", fontname=Inter, fontsize=10];

  Y [label="y_ijt — outcome\nat time t, patient j, clinic i", fillcolor="#fce7f3"];
  Fix [label="Fixed effects:\nβ0 + β1·time + β2·treatment + β3·time×treat", fillcolor="#dbeafe"];
  Pat [label="Random intercept (patient)\nu_j ~ N(0, σ_p²)", fillcolor="#fef3c7"];
  Cli [label="Random intercept (clinic)\nv_i ~ N(0, σ_c²)", fillcolor="#fef3c7"];
  Slope [label="Random slope (time | patient)\nu'_j ~ N(0, σ_s²)", fillcolor="#fef3c7"];
  Err [label="Residual ε_ijt ~ N(0, σ²)", fillcolor="#dcfce7"];

  Fix -> Y; Pat -> Y; Cli -> Y; Slope -> Y; Err -> Y;
}