Effective sample size for Burnham’s joint live/dead model

questions concerning analysis/theory using program MARK

Effective sample size for Burnham’s joint live/dead model

Postby ehileman » Tue Sep 12, 2017 9:50 am

Hi all,

I recognize that determining effective sample size for a given model is not always a straight forward issue and that it is for this very reason that effective sample size can be adjusted in program MARK. That said, I would be interested to know why the effective sample size default setting for Burnham’s joint live and dead encounters appears to be based on the number of individuals rather than the number of releases as it is in the CJS model? Any clarification folks can provide on this subject would be much appreciated.

Cheers,

Eric
ehileman
 
Posts: 32
Joined: Sat Nov 26, 2011 6:40 pm
Location: Trent University

Re: Effective sample size for Burnham’s joint live/dead mode

Postby cooch » Tue Sep 12, 2017 12:14 pm

ehileman wrote:Hi all,

I recognize that determining effective sample size for a given model is not always a straight forward issue and that it is for this very reason that effective sample size can be adjusted in program MARK. That said, I would be interested to know why the effective sample size default setting for Burnham’s joint live and dead encounters appears to be based on the number of individuals rather than the number of releases as it is in the CJS model? Any clarification folks can provide on this subject would be much appreciated.

Cheers,

Eric


As I reccall, its the same is 'live only', which is....number of animals released or re-relased during the study, excluding the last year. In other words, for a given 'cohort', total number of individual releases. For example, if you use the male Dipper data (below), there are 141 unique histories, but the ESS MARK uses is 207. For all the individuals in the first cohort, there are (6+4+8+2+5) releases, for the second cohort, there are (4+3+1+11), and so on. If you add all those up, for each cohort, you get 207.

You could confirm this is also true for live-dead by simulation (or, taking one of the example data sets from the book, and doing it by hand...).

Code: Select all
1111110 1 ; 6
1111000 1 ; 4
1100000 4 ; 8
1010000 1 ; 2
1000000 5 ; 5
0111100 1 ;  4
0111000 1 ; 3
0110000 7 ; 14
0100000 11 ; 11
0011110 1 ;  4
0011100 4 ; 12
0011000 8 ; 16
0010110 1 ; 3
0010000 11 ; 11
0001111 6 ; 18
0001110 3 ; 9
0001100 6 ; 12
0001001 1 ; 1
0001000 6 ; 6
0000111 10 ; 20
0000110 3 ; 6
0000100 9 ; 9
0000011 12 ;  12
0000010 11 ; 11
0000001 17 ; 17
/* SUM  */  207
cooch
 
Posts: 1264
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Location: Cornell University

Re: Effective sample size for Burnham’s joint live/dead mode

Postby ehileman » Tue Sep 12, 2017 4:19 pm

Hi Evan,

Thanks for the speedy reply!
As I reccall, its the same is 'live only', which is....number of animals released or re-relased during the study, excluding the last year. In other words, for a given 'cohort', total number of individual releases.

In chapter 9 (section 9.3 of Program MARK: A Gentle Introduction, 17th ed.) the simulated example dataset (LD1.INP, copied below) uses two groups, marked as as young and marked as adults. The effective sample size for this dataset is 11,866, which is identical to the number of individuals marked as young. The number of individuals marked as adults is 11,861. Based on the reduced M-array, the number of individual live releases is actually 12,476.

Code: Select all
1100000000000000  566  171;
1011000000000000   18   71;
1010110000000000    5   23;
1010101100000000    3    4;
1010101010110000    2    2;
1010101010101010    0    3;
1010101010100000    0    9;
1010101010000010    0    3;
1010101010000000    3    7;
1010101000101100    0    2;
1010101000101010    0    5;
1010101000100000    0    3;
1010101000010000    2    2;
1010101000001010    0    3;
1010101000000010    0    2;
1010101000000001    2    0;
1010101000000000    7   19;
1010100100000000    3    9;
1010100011000000    0    8;
1010100010110000    0    2;
1010100010100010    0    2;
1010100010100000    3    4;
1010100010000000    2    4;
1010100001000000    3    7;
1010100000110000    2    0;
1010100000100100    0    2;
1010100000010000    0    2;
1010100000000100    0    2;
1010100000000001    0    2;
1010100000000000   14   43;
1010010000000000   11   27;
1010001100000000    0   11;
1010001011000000    3    3;
1010001010101100    0    2;
1010001010001100    2    0;
1010001010000000    2    7;
1010001001000000    3    4;
1010001000101100    0    2;
1010001000101010    3    0;
1010001000100011    0    2;
1010001000100000    0    4;
1010001000001100    0    2;
1010001000001000    0    2;
1010001000000100    0    2;
1010001000000010    0    3;
1010001000000000    6   20;
1010000100000000    2   17;
1010000011000000    0    4;
1010000010101010    0    2;
1010000010100000    0    2;
1010000010010000    0    3;
1010000010001010    0    2;
1010000010001000    3    0;
1010000010000001    2    0;
1010000010000000    2    6;
1010000001000000    0   10;
1010000000101100    0    2;
1010000000101000    2    5;
1010000000100000    0    3;
1010000000010000    2    4;
1010000000001000    0    3;
1010000000000100    2    3;
1010000000000001    2    4;
1010000000000000   32  106;
1001000000000000   54   87;
1000110000000000    9   27;
1000101100000000    4   10;
1000101011000000    0    4;
1000101010101011    0    2;
1000101010010000    0    2;
1000101010001010    0    2;
1000101010001000    0    4;
1000101010000000    0    6;
1000101001000000    2    4;
1000101000100000    0    3;
1000101000010000    0    4;
1000101000001000    0    3;
1000101000000010    0    2;
1000101000000000    7   18;
1000100100000000    0   10;
1000100011000000    0    3;
1000100010101000    0    2;
1000100010100010    0    2;
1000100010100000    3    0;
1000100010010000    0    3;
1000100010001010    0    2;
1000100010001000    0    2;
1000100010000000    4    4;
1000100001000000    2    3;
1000100000101010    0    3;
1000100000100100    0    2;
1000100000100010    2    0;
1000100000100000    4    3;
1000100000010000    0    4;
1000100000001000    2    0;
1000100000000100    2    0;
1000100000000001    0    2;
1000100000000000    7   39;
1000010000000000   38   38;
1000001100000000    2   12;
1000001011000000    0    2;
1000001010110000    0    3;
1000001010101000    0    2;
1000001010100010    0    3;
1000001010001000    0    2;
1000001010000000    2    0;
1000001001000000    0    3;
1000001000101010    0    4;
1000001000101001    0    2;
1000001000101000    2    2;
1000001000100000    0    6;
1000001000010000    2    0;
1000001000000000    4   10;
1000000100000000   21   28;
1000000010100000    0    5;
1000000010010000    0    2;
1000000010000000    2    7;
1000000001000000   13   14;
1000000000110000    0    2;
1000000000101010    0    2;
1000000000010000    9   15;
1000000000000100   11   11;
1000000000000001    5    7;
1000000000000000  515  281;
0011000000000000  543  173;
0010110000000000   23   67;
0010101100000000    9   25;
0010101011000000    4    9;
0010101010110000    2    7;
0010101010101010    2    3;
0010101010101000    2    8;
0010101010100010    2    6;
0010101010100000    0   12;
0010101010010000    0    4;
0010101010001000    0    5;
0010101010000010    2    0;
0010101010000000    5   18;
0010101001000000    6   16;
0010101000110000    0    2;
0010101000101010    0    3;
0010101000101000    0    6;
0010101000100010    2    3;
0010101000100001    0    2;
0010101000100000    2    6;
0010101000010000    0    6;
0010101000001010    0    2;
0010101000001001    0    2;
0010101000001000    3    2;
0010101000000010    0    5;
0010101000000000   12   42;
0010100100000000   10   28;
0010100011000000    0   11;
0010100010101001    0    2;
0010100010101000    0    9;
0010100010100010    0    2;
0010100010100000    3    4;
0010100010010000    2    2;
0010100010001010    0    2;
0010100010001000    4    4;
0010100010000010    0    3;
0010100010000000    7   11;
0010100001000000    5   14;
0010100000110000    0    4;
0010100000101000    0    6;
0010100000100100    0    2;
0010100000100010    2    0;
0010100000100000    0    3;
0010100000010000    0    8;
0010100000001100    0    2;
0010100000001010    0    3;
0010100000001000    0    4;
0010100000000100    2   11;
0010100000000001    3    4;
0010100000000000   39  114;
0010010000000000   50   73;
0010001100000000    6   19;
0010001011000000    3   11;
0010001010110000    0    4;
0010001010101010    0    4;
0010001010101000    0    3;
0010001010100100    0    2;
0010001010100010    2    2;
0010001010100000    4    7;
0010001010010000    0    2;
0010001010001100    0    2;
0010001010001000    0    5;
0010001010000100    0    2;
0010001010000010    0    3;
0010001010000000    9   17;
0010001001000000    4    8;
0010001000110000    0    3;
0010001000101000    0    5;
0010001000100010    0    2;
0010001000100001    3    0;
0010001000100000    3    8;
0010001000010000    2    8;
0010001000001010    0    3;
0010001000001000    3    4;
0010001000000100    0    2;
0010001000000001    0    6;
0010001000000000   24   43;
0010000100000000   33   52;
0010000011000000    0   11;
0010000010110000    0    3;
0010000010101100    0    2;
0010000010101010    0    2;
0010000010101000    3    2;
0010000010100100    2    0;
0010000010100010    2    2;
0010000010100000    4   10;
0010000010010000    2    5;
0010000010001010    0    3;
0010000010001000    4    2;
0010000010000010    2    4;
0010000010000001    0    2;
0010000010000000    7   31;
0010000001000000   22   16;
0010000000110000    0    7;
0010000000101010    0    3;
0010000000101000    0    6;
0010000000100000    0    9;
0010000000010000   18   17;
0010000000001010    2    0;
0010000000001001    0    2;
0010000000001000    2    3;
0010000000000100    8   18;
0010000000000010    0    3;
0010000000000001   11   13;
0010000000000000  525  302;
0000110000000000  529  180;
0000101100000000   30   58;
0000101011000000    5   22;
0000101010110000    2   11;
0000101010101100    0    4;
0000101010101010    6    6;
0000101010101000    4   11;
0000101010100100    5    8;
0000101010100010    0   16;
0000101010100001    2    4;
0000101010100000    6   24;
0000101010010000    5    9;
0000101010001100    2    0;
0000101010001011    0    2;
0000101010001010    0   14;
0000101010001001    0    2;
0000101010001000    0    6;
0000101010000100    2    7;
0000101010000010    0    8;
0000101010000001    0    4;
0000101010000000   18   44;
0000101001000000   11   35;
0000101000110000    0    6;
0000101000101100    0    4;
0000101000101011    0    3;
0000101000101010    3    5;
0000101000101000    4   11;
0000101000100100    0    8;
0000101000100010    6    4;
0000101000100001    0    3;
0000101000100000    9   20;
0000101000010000    7   15;
0000101000001100    0    4;
0000101000001010    3   10;
0000101000001000    7   12;
0000101000000100    0    6;
0000101000000010    3   11;
0000101000000001    0    6;
0000101000000000   48  117;
0000100100000000   50   85;
0000100011000000    9   21;
0000100010110000    5    5;
0000100010101100    0    2;
0000100010101011    0    3;
0000100010101010    2   10;
0000100010101000    3   13;
0000100010100100    0    6;
0000100010100010    0    6;
0000100010100001    0    2;
0000100010100000    9   22;
0000100010010000    5    8;
0000100010001100    2    3;
0000100010001011    0    3;
0000100010001010    2    8;
0000100010001001    0    2;
0000100010001000    4   11;
0000100010000100    0    6;
0000100010000010    2    7;
0000100010000001    0    6;
0000100010000000   21   56;
0000100001000000   24   31;
0000100000110000    2   10;
0000100000101010    2   12;
0000100000101001    2    3;
0000100000101000    5   11;
0000100000100100    0    2;
0000100000100010    0    4;
0000100000100000    7   18;
0000100000010000   23   27;
0000100000001100    2    3;
0000100000001010    2    6;
0000100000001000    4   13;
0000100000000100   20   15;
0000100000000010    0    6;
0000100000000001   16   11;
0000100000000000  536  313;
0000001100000000  575  184;
0000001011000000   22   74;
0000001010110000    5   21;
0000001010101100    4   11;
0000001010101011    2    4;
0000001010101010    7   22;
0000001010101001    0    3;
0000001010101000   14   33;
0000001010100100    2   11;
0000001010100011    0    4;
0000001010100010    6   16;
0000001010100001    3    8;
0000001010100000   20   67;
0000001010010000   10   34;
0000001010001100    0    6;
0000001010001010    6   27;
0000001010001001    3    0;
0000001010001000    8   29;
0000001010000100    5   10;
0000001010000011    3    4;
0000001010000010    7   22;
0000001010000001    4   10;
0000001010000000   41  130;
0000001001000000   56   70;
0000001000110000    3   18;
0000001000101100    4    4;
0000001000101011    0    2;
0000001000101010    8   21;
0000001000101001    0    4;
0000001000101000    7   35;
0000001000100100    2    9;
0000001000100011    0    2;
0000001000100010    7   22;
0000001000100001    0    4;
0000001000100000   20   65;
0000001000010000   25   35;
0000001000001100    0    7;
0000001000001011    4    9;
0000001000001010    6   31;
0000001000001001    2    2;
0000001000001000   11   44;
0000001000000100   18   19;
0000001000000011    0    5;
0000001000000010    6   19;
0000001000000001   18   16;
0000001000000000  548  325;
0000000011000000  532  189;
0000000010110000   27   58;
0000000010101100    9   23;
0000000010101011    3    5;
0000000010101010   23   58;
0000000010101001    3    9;
0000000010101000   39  100;
0000000010100100    3   33;
0000000010100011    6    2;
0000000010100010   29   63;
0000000010100001    8   12;
0000000010100000   55  143;
0000000010010000   58   74;
0000000010001100    7   23;
0000000010001011    2   11;
0000000010001010   20   68;
0000000010001001    4   14;
0000000010001000   20   90;
0000000010000100   39   35;
0000000010000011    3   15;
0000000010000010   23   74;
0000000010000001   27   22;
0000000010000000  560  379;
0000000000110000  535  210;
0000000000101100   14   76;
0000000000101011    2   16;
0000000000101010   59  170;
0000000000101001    9   23;
0000000000101000   72  260;
0000000000100100   54   76;
0000000000100011    7   24;
0000000000100010   64  145;
0000000000100001   47   48;
0000000000100000  637  452;
0000000000001100  543  158;
0000000000001011   28   67;
0000000000001010  148  489;
0000000000001001   53  102;
0000000000001000  728  684;
0000000000000011  515  174;
0000000000000010  985 1326;

Unless I'm missing something (which I very well might be) or this is simply an odd coincidence, it seems that for Burnham's Joint live/dead model MARK is not using the total number of live releases as the effective sample size. Rather, MARK appears to be using the number of unique individuals from the largest group as the default setting effective sample size. Thoughts?

Eric
ehileman
 
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Location: Trent University

Re: Effective sample size for Burnham’s joint live/dead mode

Postby cooch » Tue Sep 12, 2017 5:19 pm

ehileman wrote:Hi Evan,

Thanks for the speedy reply!

In chapter 9 (section 9.3 of Program MARK: A Gentle Introduction, 17th ed.) the simulated example dataset (LD1.INP, copied below) uses two groups, marked as as young and marked as adults. The effective sample size for this dataset is 11,866, which is identical to the number of individuals marked as young. The number of individuals marked as adults is 11,861. Based on the reduced M-array, the number of individual live releases is actually 12,476.


Actually, you can't get the total number of released (which includes initial and subseuqnt) easily from the reduced m-array (although you can if you parse the full m-array output). If you look at the reduced m-array for the male dippers, and the table I posted, you'll see that the numbers used for ESS are not easily gleaned from the reduced m-array.

Unless I'm missing something (which I very well might be) or this is simply an odd coincidence, it seems that for Burnham's Joint live/dead model MARK is not using the total number of live releases as the effective sample size. Rather, MARK appears to be using the number of unique individuals from the largest group as the default setting effective sample size. Thoughts?

Eric


Well, the problem, perhaps, with that particular data set is that it has groups. I'd suggest simulating a single group -- and going from there. As per above, counting the number of 'releases' takes more work than you might wish for, if doing by hand. My assumption (based on a few years of experience) is that MARK is doing this correctly for you. But, worth simulating a small dataset, and confirming for yourself 'by hand'.

I still admit to guessing that the ESS for the live-dead is the same as for live only (since the way the saturated model likelihood for each is calculated under that assumption). But, I'll leave it to Gary to confirm.
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Re: Effective sample size for Burnham’s joint live/dead mode

Postby cooch » Tue Sep 12, 2017 5:22 pm

To save some time, here is the reduced m-array for the male doippers -- compare this to the number of 'releases' I tabulated in my first reply (with said 'releases' being the basis for the ESS):

Code: Select all
male European dippers

     Live Encounters

   Group 1 Group 1
Occ.  R(i)    j= 2     3     4     5     6     7 Total
--- ------   ----- ----- ----- ----- ----- ----- -----
  1     12       6     1     0     0     0     0     7
  2     26            11     0     0     0     0    11
  3     37                  17     1     0     0    18
  4     39                        22     0     1    23
  5     45                              25     0    25
  6     48                                    28    28
  7     46                                           0                 
cooch
 
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Location: Cornell University

Re: Effective sample size for Burnham’s joint live/dead mode

Postby gwhite » Tue Sep 12, 2017 7:35 pm

I think that the effective sample size for the Burnham live-dead model defaults to the number of releases. However, there is an option under preferences to set the effective sample size to the number of individuals. Some may have set this accidentaly and not realized it. I put this in because Ken Burnham has argued that this is the correct value for even the CJS models. I'm yet to be convinced in that the likelihood is based on the product of binomial distributions, where the sample size is clear for each.
Gary
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Re: Effective sample size for Burnham’s joint live/dead mode

Postby ehileman » Wed Sep 13, 2017 10:45 am

gwhite wrote:I think that the effective sample size for the Burnham live-dead model defaults to the number of releases. However, there is an option under preferences to set the effective sample size to the number of individuals. Some may have set this accidentaly and not realized it. I put this in because Ken Burnham has argued that this is the correct value for even the CJS models. I'm yet to be convinced in that the likelihood is based on the product of binomial distributions, where the sample size is clear for each.
Gary

Thanks for the reply, Gary. That was it! I don't recall changing the default settings for the effective sample size, but it was in fact set to the number of individuals rather than the number of releases.

Cheers!

Eric
ehileman
 
Posts: 32
Joined: Sat Nov 26, 2011 6:40 pm
Location: Trent University

Re: Effective sample size for Burnham’s joint live/dead mode

Postby ehileman » Wed Sep 13, 2017 10:55 am

Actually, you can't get the total number of released (which includes initial and subseuqnt) easily from the reduced m-array (although you can if you parse the full m-array output). If you look at the reduced m-array for the male dippers, and the table I posted, you'll see that the numbers used for ESS are not easily gleaned from the reduced m-array.

cooch wrote:To save some time, here is the reduced m-array for the male doippers -- compare this to the number of 'releases' I tabulated in my first reply (with said 'releases' being the basis for the ESS):

Code: Select all
male European dippers

     Live Encounters

   Group 1 Group 1
Occ.  R(i)    j= 2     3     4     5     6     7 Total
--- ------   ----- ----- ----- ----- ----- ----- -----
  1     12       6     1     0     0     0     0     7
  2     26            11     0     0     0     0    11
  3     37                  17     1     0     0    18
  4     39                        22     0     1    23
  5     45                              25     0    25
  6     48                                    28    28
  7     46                                           0                 

If you want to calculate the effective sample size by hand for the CJS dipper data example you provided, can't you just sum the first six releases of the reduced m-array ? i.e., 12+26+37+39+45+48 = 207
ehileman
 
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