Multistrata underestimation problem

[nwhitmore]

Hi there,

I’ve attempted to use both CJS and closed robust design multistrata procedures on a dataset to estimate survival between three states: A,B,C where the states represent proxy size classes.

What I encountered in my data was an apparent underestimate of the initial (A to B) survival parameter consistently (other survival estimates looked reasonable). I thought it might’ve been a local minima problem but neither simulated annealing nor MCMC approaches shed any light on the situation.

Finally I tried a simple test of the algorithm in a mulitstrata with recaptures only model with a simple dataset: S = 0.5, p =1, psi =1 for transitions A to B, B to C and for all other transitions psi=0 (dataset below). Testing a S(.)p(.) model where all but S is fixed parameter (p=1)I would’ve expected to get a S value around 0.5 – but I don’t (the value is S ~ 0.20). Any ideas?

Cheers,
Nathan


Naïve dataset
A00 48;
AB0 24;
ABC 12;
0A0 48;
0AB 24;
00A 48;

[cooch]

Hi there,

I’ve attempted to use both CJS and closed robust design multistrata procedures on a dataset to estimate survival between three states: A,B,C where the states represent proxy size classes.

What I encountered in my data was an apparent underestimate of the initial (A to B) survival parameter consistently (other survival estimates looked reasonable). I thought it might’ve been a local minima problem but neither simulated annealing nor MCMC approaches shed any light on the situation.

Finally I tried a simple test of the algorithm in a mulitstrata with recaptures only model with a simple dataset: S = 0.5, p =1, psi =1 for transitions A to B, B to C and for all other transitions psi=0 (dataset below). Testing a S(.)p(.) model where all but S is fixed parameter (p=1)I would’ve expected to get a S value around 0.5 – but I don’t (the value is S ~ 0.20). Any ideas?

Cheers,
Nathan


Naïve dataset
A00 48;
AB0 24;
ABC 12;
0A0 48;
0AB 24;
00A 48;

Since psi=1, this is not really a MS problem (since there is no probability that an individual who survives can remain in a given state), but, rather, is a TSM model (Chapter 7). Since all individuals are initially in state A, then the only possible transitions, which must occur on survival, are A -> B - > C. Hence, a TSM model with 3 classes.

So, you could in theory (and should, in practice) use a TSM approach for this particular analysis. But, more to the point, with only 3 occasions, you have some significant estimability problems. For 3 TSM classes (or, in your original structure, 3 states) where there is an ordinal sequencing to state transitions, you'd need at least 5 or more occasions to make everything estimable (basic rule of thumb for most problems is you need n+2 occasions for n stages). You can see this pretty quickly by looking at the PIMs for a 3 occasion study - you have only two diagonals, and this can't possibly code for all 3 stages\TSM classes.

Try the following data set, simulated with: S(A)=S(B)=S(c)=0.5, p(A)=p(B)=p(C)=1, and psi(AB)=psi(BC)=1, all other transitions psi=0.

Code: Select all

AB000 15;
ABCCC 4;
ABC00 6;
A0000 24;
ABCC0 1;
0A000 21;
0ABC0 12;
0ABCC 5;
0AB00 12;
00A00 26;
00AB0 15;
00ABC 9;
000AB 28;
000A0 22;     


Analyzing these encounter data will give you the 'correct' parameter estimates. Now, for your 'homework', modify the input full by change A, B, and C to '1', and analyze as a 3-class TSM model, constant p. You'll see you end up with the same estimates.

[nwhitmore]

Thanks Evan for putting me straight.

Cheers,
Nathan

[cooch]

Thanks Evan for putting me straight.

Cheers,
Nathan

No worries. It is worth noting that you could, in fact, us a MS approach for this sort of problem - in fact, a CJS model (TSM or otherwise) is simply a special case of a more general MS model (this is the premise - in part - behind M-SURGE) - you can use the MS approach if you're clever about the constraints, and (for certain types of problems) the choice of link functions. My general suggestion is that in most instances its easiest to go with the simplest model structure (less potential for making mistakes). So, in this case, a simple 3-class TSM model.