For capture €“ recapture experiments, Coull and Agresti (1999) used a loglinear model with exchangeable association and no higher-order terms. Explain why the model expected frequencies satisfy

log µ(y₁,..., y_T) = λ + β₁ y₁ + ... + β_T y_T + β(y₁ y₂ + y₁ y₃ + ... + y_T€“1 y_T).

Show that the fit of this model to Table 12.6 yields NÌ‚ = 90.5 and a 95% profile-likelihood confidence interval for N of (75, 125).

Table 12.6:

Results of Capture-Recapture of Snowshoe Hares Capture 3, Capture 2, Capture 1 Capture Capture Capture 5 000 001 010 011 100 101 4 110 111 3 5 (24.0) (2.3) (5.4) (0.9) (3.2) (0.5) (1.2) (0.3) 3 2 3 (4.8) (0.8) (1.8) (0.5) (1.1) (0.3) (0.6) (0.3) 4 3 (3.9) (0.6) (1.5) (0.4) (0.9) (0.2) (0.5) (0.2) 1 (1.3) (0.3) (0.8) (0.3) (0.5) (0.2) (0.4) (0.3) (6.8) (1.1) (2.6) (0.6) (1.5) (0.4) (0.9) (0.4) 4 3 1 (2.3) (0.6) (1.3) (0.5) (0.8) (0.3) (0.7) (0.4) 2 1 1 1 (1.9) (0.5) (1.1) (0.4) (0.7) (0.3) (0.6) (0.4) 2 (1.0) (0.4) (0.9) (0.5) (0.5) (0.3) (0.7) (0.7) "Values in parentheses represent the fit of the logistic-normal model. 2. 2. 2. 1. 2. 1.