Table 1.
Time-dependent functions used given a time-varying variable y. NC represents natural cubic spline function; β, fixed effects, b, random effects; and t, time.
| Model | Time-dependent functions |
| Linear and random intercept | β0 + β1tij + bi0 + εij |
| Linear and random slope | β0 + β1tij + bi0 + bi0tij + εij |
| Cubic and random intercept |
β0 + β1tij
+
 + bi0 + εij
|
| Cubic and random slope |
β0 + β1tij
+
 + bi0 + bi1tij + εij
|
| Spline and random intercept | NC(tij, 2, (β0, β1, β2, β3)T, (bi0) +εij) |
| Spline and random slope | NC(tij, 2, (β0, β1, β2, β3)T, (bi0, bi1)T +εij) |
| Spline and random spline | NC(tij, 2, (β0, β1, β2, β3)T, (bi0, bi1, bi2, bi3)T +εij) |