How is the focus different for the model in Problem 12.3 than for the loglinear model (AC, AM, CM) used in Section 8.2.4? If ÏÌ

How is the focus different for the model in Problem 12.3 than for the loglinear model (AC, AM, CM) used in Section 8.2.4? If σ̂ = 0, which loglinear model has the same fit as the GLMM?

Data from Problem 12.3:

For table 8.3, let y_it = 1 when subject i used substance t. Table 12.11 shows output for the logistic-normal model

logit[P(Y_it = 1|u_i)] = u_i + β_t.

Interpret. Illustrate by comparing use of cigarettes and marijuana.

Table 8.3:

Table 12.11:

Alcohol, Cigarette, and Marijuana Use for High School Seniors Marijuana Use Alcohol Cigarette Use Use Yes No 911 Yes Yes 538 No 44 456 No Yes 3 43 No 279 2. Output Description Subjects Max Obs Per Subject Value Std Error 0.1824 Parameter betal beta2 beta3 Estimate 4.2227 1.6209 -0.7751 3.5496 2276 t Value 23.15 Parameters Quadrature Points Log Likelihood 0.1207 13.43 200 0.1061 0.1627 -7.31 21.82 -3311 sigma