Refer to correlation model (9.16) (Goodman 1985, 1986). a. Show that is the correlation between the

Refer to correlation model (9.16) (Goodman 1985, 1986).

a. Show that λ is the correlation between the scores.

b. If this model holds, show that ∑_i µ_i (π_ij/π_+j) = λv_j and ∑_j υ_j (π_ij/π_i+) = λµ_i. Interpret.

c. With λ close to zero, show that log(π_ij) has form γ_i + δ_i + λ µ_i υ_j + _O(λ), where _O(λ)/λ → 0 as λ → 0. Thus, when the association is weak, the correlation model is similar to the linear-by-linear association model with β = λ and scores {µ_i = µ_i} and {υ_j = υ_j}.