A correlation four visits cannot have
An exchangeable correlation is proposed for the four visits of one child, with pairwise correlation -0.5.
Why can that not be the correlation of those four visits?
Worked answer
An exchangeable correlation matrix for K visits has eigenvalues 1-\rho, repeated K-1 times, and 1+(K-1)\rho once. Both are nonnegative only when -1/(K-1)\le\rho\le 1. For four visits the lower bound is -1/3. A value of -0.5 is below that bound, so the matrix is not a correlation matrix: no such set of four random variables exists. A report of a working correlation at or below the bound is the constraint, not a precise estimate of a correlation the visits cannot have. The independent unit remains the child. Treating the visits as if each were a different child uses the wrong unit.