! Schwarz, C.J. and Arnason, A.N. (2000). ! Estimation of age-specific breeding probabilities from capture-recapture data. ! Biometrics 56, 59-64. ! ! This illustrates the fitting of a linear function to a set of parameters ! It is the gull date from Clobert et al (Biometrics 1994) ! refered to in our paper on estimating breeding proportions ! !---------------------------------------------------------------------------- ! This first model has ! capture probabilites a linear (on logit scale) function of number of visits ! survival probabilities constant over time and cohorts ! separate breeding probabilities for each cohort. ! This corresponds to the left hand side of Table 2 ! except the table in the paper had a linear function on the standard prob not on the logit scale. ! The results are very similar. Gull data from Clobert et al. - p(logit-linear) phi(constant) breed(g*t) 3 8 notrace stat pim design noinit logit logit logit c1 = (7.0,5.0,9.0,9.0,7.0,8.0,9.5,9.5)=number of visits 1 2 0 2 0 0 group 1 statistics 2 3 0 3 0 0 3 4 0 4 1 0 4 7 0 7 3 1 5 5 2 5 2 2 6 4 1 4 1 3 7 4 2 4 2 2 8 8 4 8 0 0 1 0 0 0 0 0 group 2 statistics 2 0 0 0 0 0 3 5 0 5 3 0 4 8 2 8 5 1 5 7 4 7 2 2 6 5 1 5 1 3 7 4 1 4 1 3 8 6 4 6 0 0 1 0 0 0 0 0 group 3 statistics 2 0 0 0 0 0 3 5 0 5 1 0 4 8 1 8 1 0 5 3 1 3 0 0 6 6 0 6 1 0 7 8 1 8 0 0 8 3 0 3 0 0 ! The PIM matrices ! 1 2 3 4 5 6 7 8 <- sample times 1 2 3 4 5 6 7 8 <- group 1 10 10 10 10 10 10 10 <- group 1 phi constant after first year of banding 16 17 18 19 20 20 20 20 24 2 3 4 5 6 7 8 <- group 2 p equal to group 1 except for first sample time 32 10 10 10 10 10 10 <- group 2 phi constant after first year of banding 39 40 41 42 43 20 20 20 47 48 3 4 5 6 7 8 <- group 3 p equal to group 1 except for first sample times 55 56 10 10 10 10 10 <- group 3 phi constant after first year of banding 62 63 64 65 66 67 20 20 2 beta parameters 1 0 1 7.0 p(1)--p(8) linear function of number of visits (on logit scale) 2 0 1 5.0 3 0 1 9.0 4 0 1 9.0 5 0 1 7.0 6 0 1 8.0 7 0 1 9.5 8 0 1 9.5 24 -10 0 0 p(2,1) = 0 47 -10 0 0 p(3,1) = 0 48 -10 0 0 p(3,2) = 0 32 10 0 0 phi(2,1) = 1 55 10 0 0 phi(3,1) = 1 56 10 0 0 phi(3,2) = 1 20 -10 0 0 pent(1,4)--pent(1,7), pent(2,5)--pent(2,7), pent(3,6)--pent(3,7) = 0 as no births after age 5 39 -10 0 0 pent(2,0) = 0 animals don't breed yet 62 -10 0 0 pent(3,0) = 0 animals don't breed yet 63 -10 0 0 pent(3,1) = 0 0 0 0 0 end of design matrix specifications !---------------------------------------------------------------------------- ! This second model has ! capture probabilites a linear (on logit scale) function of number of visits ! survival probabilities constant over time and cohorts ! common breeding probabilities for each cohort. ! This corresponds to the right hand side of Table 2 ! except the table in the paper had a linear function on the standard prob not on the logit scale. ! The results are very similar. Gull data from Clobert et al. - p(logit-linear) phi(constant) breed(t) 3 8 notrace stat pim design noinit logit logit logit c1 = (7.0,5.0,9.0,9.0,7.0,8.0,9.5,9.5); 1 2 0 2 0 0 group 1 statistics 2 3 0 3 0 0 3 4 0 4 1 0 4 7 0 7 3 1 5 5 2 5 2 2 6 4 1 4 1 3 7 4 2 4 2 2 8 8 4 8 0 0 1 0 0 0 0 0 group 2 statistics 2 0 0 0 0 0 3 5 0 5 3 0 4 8 2 8 5 1 5 7 4 7 2 2 6 5 1 5 1 3 7 4 1 4 1 3 8 6 4 6 0 0 1 0 0 0 0 0 group 3 statistics 2 0 0 0 0 0 3 5 0 5 1 0 4 8 1 8 1 0 5 3 1 3 0 0 6 6 0 6 1 0 7 8 1 8 0 0 8 3 0 3 0 0 ! The PIM matrices ! 1 2 3 4 5 6 7 8 <- sample times 1 2 3 4 5 6 7 8 <- group 1 10 10 10 10 10 10 10 <- group 1 phi constant 16 17 18 19 20 20 20 20 24 2 3 4 5 6 7 8 <- group 2 p equal to group 1 except for first sample time 32 10 10 10 10 10 10 <- group 2 phi constant 39 16 17 18 19 20 20 20 47 48 3 4 5 6 7 8 <- group 3 p equal to group 1 except for first sample times 55 56 10 10 10 10 10 <- group 3 phi constant 62 63 16 17 18 19 20 20 2 beta parameters 1 0 1 7.0 p(1)--p(8) linear function of number of visits (on logit scale) 2 0 1 5.0 3 0 1 9.0 4 0 1 9.0 5 0 1 7.0 6 0 1 8.0 7 0 1 9.5 8 0 1 9.5 24 -10 0 0 p(2,1) = 0 47 -10 0 0 p(3,1) = 0 48 -10 0 0 p(3,2) = 0 32 10 0 0 phi(2,1) = 1 55 10 0 0 phi(3,1) = 1 56 10 0 0 phi(3,2) = 1 20 -10 0 0 pent(1,4)--pent(1,7), pent(2,5)--pent(2,7), pent(3,6)--pent(3,7) = 0 as no births after age 5 39 -10 0 0 pent(2,0) = 0 animals don't breed yet 62 -10 0 0 pent(3,0) = 0 animals don't breed yet 63 -10 0 0 pent(3,1) = 0 0 0 0 0 end of design matrix specifications