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:

Transcribed Image Text:

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