Refer to Problem 12.7. Let µk(a, b, c) denote the

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

log µ_k(a, b, c) = aβ_A + bβ_B + cβ_C + λ_k(a, b, c),

where λ_k(a, b, c) = λ_k(a, c, b) = λ_k(b, a, c) = λ_k(b, c, a) = λ_k(c, a, b) = λ_k(c, b, a). Fit the model, and show that β̂_B – β̂_A = 1.64 (SE = 0.34), β̂_C – β̂_A = 2.23 (SE = 0.39), β̂_C – β̂_B = 0.59 (SE = 0.39). Interpret. Compare results with Problem 12.7 for model (12.19).

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: