Refer to Problem 12.7. Let k (a, b, c) denote the expected frequency of outcomes (a, b, c) for treatments (A, B, C) under

Refer to Problem 12.7. Let μ_k(a, b, c) denote the expected frequency of outcomes (a, b, c) for treatments (A, B, C) under treatment sequence k, where outcome 1 = relief and 0 = nonrelief. With a nonparametric random effects approach, show that one can estimate treatment effects in model (12.19) by fitting the quasi-symmetry model

Data from Problem 12.7:

For the crossover study in Table 11.10 (Problem 11.6), fit the model

logit[P(Y_i(k)t = 1|u_i(k))] = α_k + β_t + u_i(k),

where {u_i(k)} are independent N(0, σ²). Interpret {β̂_t} and σ̂.

Table 11.10:

Response Pattern for Treatments (A, B, C) 100 Treatment Sequence 001 101 110 011 000 010 111 2 2 1 ABC 2 4 AC B BA C B C A 3 1 1 1 CAB 5 3 CBA 4