Consider the conditional symmetry (CS) model (10.28).

a. Show that it has the loglinear representation

log µ_ab = λ_{min(a, b), max(a, b)} + τI( a

where I(·) is an indicator.

b. Show that the likelihood equations are

c. Show that τ̂ = log [(∑ ∑_{a nab)/(∑ ∑a > b nab)], µ̂aa = naa, a = 1,..., I, µ̂ab = exp[τ̂I(a ab} + n_ba)/[exp(τ̂) + 1] for a ≠ b.

d. Show that the estimated asymptotic variance of τ̂ is

e. Show that residual df = (I + 1)(I – 2)/2.

f. Show that conditional symmetry + marginal homogeneity = symmetry. Explain why G²(S | CS) tests marginal homogeneity (df = 1). When the model holds G²(S | CS) is more powerful asymptotically than G²(S | QS). Why?