Sex covariate in closed capture-recapture

[jimborbs]

Hi,

I have data where I want to incorporate the animal's (leopards) sex as covariate to determine if it affects capture recapture probabilities in Huggins model. Now the problem I am facing is that I have certain identified individuals whose sex is unknown (since the pictures I got missed out the back part) and I am not certain how should I code them? I am using 1, 0 for males and 0, 1 for females as coding. Should the coding for unknown be 0, 0? Would MARK take into account those unknown covariate and estimate p and c based on the animals with known sex only?

Any assistance would be of great help.
Thanks.
Jim

[gwhite]

First, you don't need to use 2 covariates to code sex. Either code a variable with 1 for males and 0 for females, or vice versa. However a trick to handle the unknown sex animals in a single covariate is to use females = 1, males = -1, and unknown = 0. The the beta value is added for females, subtracted for males, and left out for unknown.

Gary

[jimborbs]

Thanks for the tip Gary.

[jimborbs]

Hi Gary,

I have been unable to use -1 as a covariate code in the program. MARK says the encounter history format should contain only 1 and 0 when I use -1 as a code for females (or males). Am I missing something while providing the input file or am I not doing it correctly?

[cooch]

Hi Gary,

I have been unable to use -1 as a covariate code in the program. MARK says the encounter history format should contain only 1 and 0 when I use -1 as a code for females (or males). Am I missing something while providing the input file or am I not doing it correctly?

Post the first few lines of your input file. It should look something like this:

10001101 1 1;
10110111 1 -1;
11101111 1 0;

and so on, where the first string is the encounter history, the second number is the frequency, and the final (right-most) number is the covariate (1, -1, or 0, respectively, for these three histories).

This is all covered in some detail in chapter 2 (basic formatting of the input file) and chapter 11 (specific details for individual covariates.

[jimborbs]

Thanks. Its working now. I think the inp file was not formatted properly.

[jCeradini]

Hi Gary and Evan,

I understand how to code the inp file with 1, -1, and 0, and it seems like a nice alternative to using the mean for individuals with missing values in categorical covariates. What I'm confused about is how it changes the interpretation of, e.g., a 'sex effect' when coded with F = 1, M = -1, and unknown = 0?

Thanks!
Joe Ceradini
University of Wyoming

[gwhite]

Joe:
In your case, females have the beta effect added, males have it subtracted, and animals with unknown gender have no change. So, 2 times the beta estimate is the difference between females and males.

If you had no unknowns, and coded females = 1 and males = 0, then the resulting estimate of beta under this model would be 2X the estimate of beta using the 1, 0, -1 coding.

Gary

[jCeradini]

Thanks Gary! Makes sense to me now.

- Joe

[jhines]

It seems that doing it that way forces the proportion of unknowns to be 50% male. Why not use the Huggins/mixture model and let MARK estimate the proportion of males in the unknown group. You could enter the data as 3 groups (M, F, U) and set the two rows of pims for p equal for M and F, and the first row for U = the pim value for p for M, and the 2nd row for U= the pim value for p for F. Fix pi for M and F to any value (since p1=p2). Here's how the MARK input file might look:

Code: Select all

proc estimate link=Sin varest=2ndPart ;  model={pi(),p(g)}2};
      fixed=1;  parm(1)=.314159;
     group=1 pi rows=1 cols=1 Square Constant=1;
     group=2 pi rows=1 cols=1 Square Constant=1;
     group=3 pi rows=1 cols=1 Square Constant=2;
     group=1 p rows=2 cols=1 Square Constant=3;
     group=2 p rows=2 cols=1 Square Constant=4;
     group=3 p rows=2 cols=1 Square;     3;  4;
     design matrix constraints=4 covariates=4 identity;

So, we've fixed parameter #1 (pi for M and pi for F = .314159). We're estimating parameter #2 (pi for Unknowns), parameter 3 (p for Males), parameter #4 (p for Females). The 2 heterogeneous groups for Unknown use the M and F p parameters (3 and 4).

My only concern is that I suspect that you don't have recaptures in the unknown group, since it seems unlikely that the same individual would hide his/her rear end from the camera on multiple visits.

Jim