Table 1 Simulation results for registration system with two occasions. p11 is the probability for capture at occasion 1 and occasion 2, p10 is the probability for capture at occasion 1 but not at occasion 2, and so forth. The marginal probabilities for capture at occasion 1 and 2 are p1=p11+p10 and p2=p11+p01, respectively. In settings 1 to 6 inclusion on occasion 1 is independent of inclusion on occasion 2. In settings 7 and 8, occasions become dependent (odds ratio larger than 1) but the conditional probability for capture at occasion 2 given no capture at occasion 1 is identical to the unconditional probability for capture at occasion 1, the capture-removal estimator works fine. In settings 9 and 10, those conditional and unconditional probabilities are different and the capture-removal estimator breaks down
LP | Chapman | Removal | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Setting | p 1 | p 2 | p 11 | p 10 | p 01 | p 00 | \(\bar N_{\textit {LP}}\) | SD | \(\bar N_{\textit {Ch}}\) | SD | \(\bar N_{R}\) | SD |
1 | 0.5 | 0.5 | 0.25 | 0.25 | 0.25 | 0.25 | 1001 | 31 | 1000 | 31 | 1007 | 59 |
2 | 0.3 | 0.3 | 0.09 | 0.21 | 0.21 | 0.49 | 1006 | 77 | 1000 | 76 | 1064 | 262 |
3 | 0.5 | 0.6 | 0.30 | 0.20 | 0.30 | 0.20 | 1002 | 27 | 1001 | 27 | 1271 | 113 |
4 | 0.3 | 0.35 | 0.105 | 0.195 | 0.245 | 0.455 | 1004 | 66 | 1000 | 65 | 1825 | 6475 |
5 | 0.5 | 0.3 | 0.15 | 0.35 | 0.15 | 0.35 | 1000 | 48 | 998 | 47 | 714 | 21 |
6 | 0.3 | 0.1 | 0.03 | 0.27 | 0.07 | 0.63 | 1021 | 155 | 999 | 146 | 392 | 17 |
7 | 0.5 | 0.55 | 0.30 | 0.20 | 0.25 | 0.25 | 955 | 28 | 955 | 28 | 1003 | 57 |
8 | 0.5 | 0.625 | 0.375 | 0.125 | 0.25 | 0.25 | 834 | 18 | 834 | 18 | 1009 | 56 |
9 | 0.3 | 0.1 | 0.065 | 0.235 | 0.035 | 0.665 | 464 | 34 | 462 | 34 | 340 | 15 |
10 | 0.5 | 0.5 | 0.4 | 0.1 | 0.1 | 0.4 | 625 | 17 | 626 | 17 | 625 | 17 |