A first-order Markov chain has stationary (or time-homogeneous) transition probabilities if the one-step transition probability matrices are identical, that is, if for all i and j,

π_j|i(1) = π_j|i(2) = ... = π_j|i(T) = π_j|i.

Let X, Y, and Z denote the classifications for the I × I × T table consisting of {n_ij(t), i = 1..., I, j = 1,..., I, t = 1,..., T}.

Explain why all transition probabilities are stationary if expected frequencies for this table satisfy loglinear model (XY, XZ). [Thus, the likelihood-ratio statistic for testing stationary transition probabilities equals G² for testing fit of model (XY, XZ).]