Refer to correlation model (9.16) (Goodman 1985, 1986). a. Show that is the correlation between the scores. b. If this model holds, show that

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}.