For Problem 12.7, fit the more general GLMM having treatment effects {β_tk} that vary by sequence. Test whether the fit is better. One could also consider period or carryover effects. Add two period effects to model (12.19) (e.g., the first-period-effect parameter adds to the model when t = A and k = 1, 2, t = B and k = 3, 4, and t = C and k = 5, 6). Check whether the fit improves. Interpret.

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