GOF test difficulties

[SandraChristine]

Hi,
I'm working with live recapture, dead recovery and resighting information for a number of abalone populations (I'm using the Both(Barker) option in MARK). When I try to run goodness of fit tests on the general model, I run into difficulties. The bootstrapping GOF option in MARK returns negative values for all df, while the median c-hat option does not successfully complete any simulations. I have included one set of data with which I am encountering these problems. There are 5 encounter occasions, only one site, and the general model is S(t) p(t) r(t) R(t) R'(t) F(t) F'(t). Does anyone know what I'm doing wrong/ have suggestions? Thank-you, Christine.

1000000000 145;
1000000002 1;
1000000200 5;
1000010000 6;
1001000000 2;
1000100000 21;
1000020000 3;
1010000000 7;
1010001000 1;
1010100000 3;
1010021000 1;
1000000100 1;
1000000010 2;
1000100010 1;
1010000010 1;

[sbonner]

Hey Christine,

I think that the problem here is that the general model you have selected simply has too many parameters. The general principal of mark-recapture modelling is that you're fitting a multinomial distribution to the counts of each observed capture history. The model you have specified has 31 parameters, but there are only 15 unique capture histories in you data set, so there are going to be unidentifiable parameters. This is also confirmed by the fact that a lot of the real estimates are on the boundary of the parameter space -- equal to 0 or 1. I tried fitting a reduced model with no movement (F(t)=1 and F'(t)=0 for all occasions), and this model not only fit the data much better but it also produced sensible results for the bootstrap GOF. The median c-hat procedure still failed, but I noticed that several of the parameter estimates are still close to 0 or 1. An even more restricted model with constant r and constant R'=R produced an even better fit, and the median c-hat procedure also worked, but I have no idea if this is biologically plausible.

My suggestion is that your going to have to use a more restricted model to compute the c-hat adjustment. While it's generally recommended to use a general model to do this, the data is just to sparse in your case. Should be OK, but probably worth noting in any publication that you were forced to use a more restricted model. Not an abalone expert, so I don't know if the models I've described make any sense at all -- Wikipedia couldn't even tell me if they move!

Hope that helps!