In addition to the obvious relationships between y 1 and y 2 through ρ 1 and δ 1 , model (1) also assumes that once y 1 has been observed at point x, no other observation of y 1 at any x = x furthers our knowledge about the higher level response y 2 (x). That is, Cov(y 1 (x ), y 2 (x)|y 1 (x)) = 0, a natural Markov property for multi-level responses.