MAS-II: Random intercepts create dependence within a group
A random-intercept model allows observations in the same group to share a latent effect. That makes them correlated even if the residual errors are independent conditional on the group effect. Repeated observations are not automatically independent data points.
Worked example or practice scenario
In Y_ij=β0+b_i+ε_ij, let Var(b_i)=4 and Var(ε_ij)=12. Each observation has variance 16, and two observations in the same group have covariance 4. The intraclass correlation is 4/16=.25.
Try this next
Compare observations from different independent groups: their covariance from the group effect is zero. State whether a requested prediction concerns an existing group with observed history or a new group; the available information differs.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.