## Median C-Hat

questions concerning analysis/theory using program MARK

### Median C-Hat

Has anyone ever calculate a negative C-Hat estimation for CJS? I assume this has something to do with overparameterized model for phi(t)p(t)? Any advice would be greatly appreciated.

10000 449;
10001 5;
10010 4;
10100 2;
10100 -1;
10110 -1;
11000 5;
11000 -1;
11001 2;
11010 1;
11011 2;
11100 4;
11101 1;
Fish_Boy

Posts: 63
Joined: Fri Oct 28, 2005 2:12 pm
Location: Winnipeg

### Re: Median C-Hat

Fish_Boy wrote:Has anyone ever calculate a negative C-Hat estimation for CJS? I assume this has something to do with overparameterized model for phi(t)p(t)? Any advice would be greatly appreciated.

10000 449;
10001 5;
10010 4;
10100 2;
10100 -1;
10110 -1;
11000 5;
11000 -1;
11001 2;
11010 1;
11011 2;
11100 4;
11101 1;

Fletcher chat {phi(t)p(t)} = 1.7452813
RELEASE: 3.3157/6 = 0.553
median c-hat (10 design points, 100 replicates per design point, upper bounrd = 3) = 3.45

If you let median c-hat go from 1-5 (default), you can get a negative value.

The significant variation in estimates among the 3 methods (above), reflects the fact that you have basically no data, and you're working with only a single cohort. If you look at the reduced m-array (below), you have ~9% total recaptures. There isn't enough there for MARK to simulate the bootstrapped samples, which is why the median-c-hat is 'flaky'. And, the Fletcher c-hat has issues with losses on capture, so that is suspect. This is also reflected in the real parameter estimates, which are basically trash, by and large.

Best you can do is set p = constant, and hold your nose. But hold it tight, because even estimates from {phi(t)p(.)} are basically garbage.

Code: Select all
`   Group 1 Group 1Occ.  R(i)    j= 2     3     4     5 Total--- ------   ----- ----- ----- ----- -----  1    478      16     4     4     5    29  2     15             5     3     2    10  3      8                   1     1     2  4      7                         2     2  5     10                               0    `
cooch

Posts: 1460
Joined: Thu May 15, 2003 4:11 pm
Location: Cornell University

### Re: Median C-Hat

So I pooled all the cohorts into a single encounter history. 7 occasions, 4 groups, and time intervals 3 for interval 1 and 1 for remaining intervals.

0001000 0 0 0 762;
0001001 0 0 0 23;
0001010 0 0 0 28;
0001011 0 0 0 11;
0001100 0 0 0 22;
0001101 0 0 0 6;
0001110 0 0 0 7;
0001111 0 0 0 1;
0010000 0 0 449 0;
0010001 0 0 5 0;
0010010 0 0 4 0;
0010100 0 0 3 0;
0010110 0 0 1 0;
0011000 0 0 6 0;
0011001 0 0 2 0;
0011010 0 0 1 0;
0011011 0 0 2 0;
0011100 0 0 4 0;
0011101 0 0 1 0;
0100000 0 439 0 0;
0100001 0 5 0 0;
0100010 0 1 0 0;
0100011 0 1 0 0;
0100100 0 4 0 0;
0101000 0 13 0 0;
0101100 0 1 0 0;
0110000 0 17 0 0;
0110001 0 1 0 0;
0110010 0 4 0 0;
0110100 0 2 0 0;
0110101 0 1 0 0;
0111000 0 7 0 0;
0111100 0 2 0 0;
1000000 330 0 0 0;
1000001 8 0 0 0;
1000010 9 0 0 0;
1000010 -1 0 0 0;
1000100 17 0 0 0;
1000101 2 0 0 0;
1000110 2 0 0 0;
1001000 34 0 0 0;
1001000 -2 0 0 0;
1001001 2 0 0 0;
1001001 -1 0 0 0;
1001010 3 0 0 0;
1001011 1 0 0 0;
1001100 5 0 0 0;
1001110 1 0 0 0;
1010000 21 0 0 0;
1010000 -1 0 0 0;
1010001 2 0 0 0;
1010010 3 0 0 0;
1010011 1 0 0 0;
1010100 4 0 0 0;
1011000 9 0 0 0;
1011000 -1 0 0 0;
1011010 1 0 0 0;
1011100 2 0 0 0;

I get a similar issue with C-Hat for the full model, but reasonable survival estimates for constant survival by group and time varying recapture. However, the support for the constant survival is low compared with full model.

COMBINED_COHORTS

Real Function Parameters of {CONSTANT_PHI_TIME_P}
95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
-------------------------- -------------- -------------- -------------- --------------
1:Phi 0.8626455 0.0206212 0.8170261 0.8983066
2:Phi 0.4801478 0.0458523 0.3918600 0.5696932
3:Phi 0.3697552 0.0286015 0.3156520 0.4273410
4:Phi 0.3983637 0.0365684 0.3293026 0.4717216
5:p 0.9992007E-015 0.2596382E-008 -0.5088907E-008 0.5088909E-008
6:p 0.1761729 0.0286778 0.1267753 0.2395382
7:p 0.2814561 0.0435091 0.2044159 0.3738860
8:p 0.1757301 0.0365752 0.1150200 0.2591026
9:p 0.1357748 0.0345792 0.0810300 0.2187034
10:p 0.1223775 0.0359336 0.0674919 0.2117613
11:p 0.4503428 0.1848149 0.1594041 0.7797306
12:p 0.1453030 0.0274342 0.0993113 0.2076826
13:p 0.1997819 0.0520397 0.1165343 0.3208977
14:p 0.1755548 0.0676317 0.0785202 0.3473079
15:p 0.2142006 0.1060345 0.0734736 0.4837404
16:p 0.5948180 0.3083897 0.1067814 0.9474439
17:p 0.4502768 76.818517 0.5544218E-264 1.0000000
18:p 0.4502053 64.130142 0.2350391E-220 1.0000000
19:p 0.0927171 0.0235924 0.0556927 0.1504340
20:p 0.1367328 0.0468127 0.0678611 0.2562844
21:p 0.3055910 0.1023765 0.1459908 0.5311524
22:p 1.0000000 0.1432005E-004 0.9999719 1.0000281
23:p 0.4503081 73.321308 0.5936608E-252 1.0000000
24:p 0.4501509 159.86438 0.8071929E-304 1.0000000
25:p 0.4500340 173.60430 0.8068117E-304 1.0000000
26:p 0.1058683 0.0193301 0.0735156 0.1501513
27:p 0.3405569 0.0688335 0.2207060 0.4849869
28:p 0.7457548 0.2103678 0.2500139 0.9626995
Fish_Boy

Posts: 63
Joined: Fri Oct 28, 2005 2:12 pm
Location: Winnipeg