Missing Data in the Huggins Closed Capture Model

[brp]

We have fox trapping data. We have 12 grids of 40 traps each, but due to safety concerns, grid #7 and 7 traps from grid #4 were not sampled. Grids are sampled on 4 consecutive days. We plan to use the Huggins Closed Capture Model because we want to include 3 covariates in the model. Estimating abundance is of primary interest.

I am wondering how to best handle the missing data.
I plan to run 2 analyses using different grouping factors:

1) By Grid

· Here, I can enter the 12 grids as groups and constrain p=c=0 for grid 7. To do this, do I need to have one row in the encounter history file specifying grid 7? Something like this – where I have 4 dots representing the 4 occasions of missing data, a code for grid 7, and 3 dots for the missing values of the covariates?

.... 0 0 0 0 0 0 1 0 0 0 0 0 . . . ;

· How can I deal with the missing data on 7 traps of grid 4 since grids (not traps) are the groups?

We would like our grid results to be comparable, but having 7 fewer traps being sampled on one grid creates a problem. Is there a way to achieve comparable grid results?

2) By Habitat

· There are 4 habitat types, with (usually) 3 grids contained in each. But since grid 7 was not sampled, there are only 2 grids sampled in one of habitats. Should I simply not enter anything in the encounter history file for grid 7?

My habitat results are also incomparable, due to a difference in sample size and therefore precision. Is there a way to achieve comparable habitat results?

· How can I deal with the missing data on 7 traps of grid 4 since habitats (not traps or grids) are the groups?

Your thoughts are greatly appreciated!

[sbonner]

Hey brp,

I'm a little confused by your question, so perhaps I'm not understanding correctly. You say that grid 7 wasn't sampled -- ever? In this case, it will never appear in your capture history file since you can't have any individuals that were captured on the grid. What I'm confused by is that you seem to be talking about creating a capture history for a specific grid:

Something like this – where I have 4 dots representing
the 4 occasions of missing data, a code for grid 7, and 3 dots for the
missing values of the covariates?

.... 0 0 0 0 0 0 1 0 0 0 0 0 . . . ;

Capture histories should not refer to specific traps, but rather to specific individuals. If you weren't interested in variations in capture probability over traps within grids or over days, then you could make each capture history a vector of 12 0's and 1's with each grid as a capture occasion. This would allow you to estimate capture probabilities separately for each grid and then to relate these the covariates. However, since sampling was done at grid 12 you would want to fix the capture probability for that grid to 0. Alternatively, you could simply remove this from the capture histories altogether and simply use vectors of 11 0's and 1's to represent the sampled grids.

The fact that there were only 33 traps operating on the grid #4 will correct itself if you allow the capture probabilities to vary by grid. Alternatively, you could use the number of traps as a covariate to model the capture probability -- effectively, number of traps is a measure of effort.

Hope that I've understood properly and that this helps with your problem.

Cheers,

Simon

[murray.efford]

Coming rather late to this...
Assuming your interest is in abundance (in the sense of density) and not survival, I suggest you consider spatially explicit capture-recapture. This deals naturally with problems of incomplete grid setting (search for help on 'usage' in Density or 'secr') and has other advantages. Treat grids as 'sessions' and habitat as a session-level covariate. Simon's solution for the partial setting suffers from the technical catch that N is likely also to be different if you used a different trap array (although not by much in this case).
Murray

[brp]

Thanks Simon.

Grid 7 was sampled in 2007-2009, but not sampled in 2010. I want the capture histories to be for individual foxes, not for a trap or grid. I lend us down the wrong path there - sorry.

Good idea on how to deal with grid 4. Your input definitely helped.

Thanks,
Becky