Loglinear model M 0 is a special case of loglinear model M 1 . a. Haberman (1974a) showed that when { i } satisfy any

Loglinear model M₀ is a special case of loglinear model M₁.

a. Haberman (1974a) showed that when {µ̂_i} satisfy any model that is a special case of M₀, ∑_i µ̂_1i log µ̂_i = ∑_i µ̂_0i log µ̂_i. Thus, µ̂₀ is the orthogonal projection of µ̂₁ onto the linear manifold of {log µ} satisfying M₀. Using this, show that G²(M₀) – G²(M₁) = 2∑_i µ̂_1i log(µ̂_1i/µ̂_0i).