I am confused about the relationship between the beta parameter estimates and the real parameter estimates for the abundance parameters in POPAN and Jolly-Seber Lambda -- Burnham models. For a model with only intercept term and log link function I thought the relationship should be N_real = exp(Beta_N). What is the relationship between the model parameter estimates and the values on the real scale?
For example, running a POPAN model on dipper data with log link function the coefficient is 2.72 and the real estimate is 309.
PARM-SPECIFIC Link Function Parameters of { Phi(~1)p(~1)pent(~1)N(~1) }
95% Confidence Interval
Parameter Beta Standard Error Lower Upper
------------------------- -------------- -------------- -------------- --------------
1:Phi:(Intercept) 0.2382585 0.1016105 0.0391019 0.4374150
2:p:(Intercept) 2.2914677 0.3323917 1.6399799 2.9429554
3:pent:(Intercept) 0.6683266 0.2233367 0.2305866 1.1060667
4:N:(Intercept) 2.7195525 0.4296113 1.8775143 3.5615907
Real Function Parameters of { Phi(~1)p(~1)pent(~1)N(~1) }
95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
-------------------------- -------------- -------------- -------------- --------------
1:Phi g1 a0 t1 0.5592844 0.0250455 0.5097742 0.6076429
2:p g1 a0 t1 0.9081679 0.0277211 0.8375322 0.9499295
3:N g1 a0 t1 309.17353 6.5187202 300.77275 327.99446
4:pent g1 a1 t2 0.1535493 0.0026990 0.1483335 0.1589143
5:pent g1 a2 t3 0.1535493 0.0026990 0.1483335 0.1589143
6:pent g1 a3 t4 0.1535493 0.0026990 0.1483335 0.1589143
7:pent g1 a4 t5 0.1535493 0.0026990 0.1483335 0.1589143
8:pent g1 a5 t6 0.1535493 0.0026990 0.1483335 0.1589143
9:pent g1 a6 t7 0.1535493 0.0026990 0.1483335 0.1589143
EDIT:
I ran the JS model on the dipper data using marked package in R and coefficient of N is 2.72 and the estimated real value of N is 15.17. This agrees with my expectations that N_real = exp(Beta_N). Is there a bug in MARK or am I doing something wrong?