Incorporating distance as covariate in "Removal" s

[Manuel]

Hi All,

I am using MARK (Huggins closed captures) to analyze data on bobwhite counts collected under a "removal" sampling (time to detection) approach (3 equal time intervals). I am considering different observer as categorical covariate, but because I also have distance information (radial distance from the point survey to the bird) I would like to incorporate distances to the data. The distances were measured in distance categories, so I have 7 distance categories (mid-points): 25, 75, 125, 175, 250, 350, and 450 m. The goal of the analysis is only to estimate detection probability (p).
Do I need to include the information on distance as categorical or continuous covariate?
Thank you very much in advance.

Manuel

[bmitchel]

Manuel -

Your distance covariate can be analyzed as either categorical (i.e. 6 binary variables) or continuous (1 variable using the midpoint distance).

Analyzing as a categorical variable requires estimating a lot of parameters, but makes no assumption about functional form of the relationship with distance. In other words, by estimating each distance bin separately you have the possibility (for example) of finding that the first and fourth distance classes produce a much lower probability of detection than the other classes.

Analyzing as a continuous covariate makes an assumption about the functional form, but has the benefit of taking many fewer parameters to estimate. Depending on how you code your categories, you are basically assuming a linear relationship between detection probability and distance. In other words, if you rescale your data to keep the values between 0 and 1 by dividing all of your distances by 500 (because MARK performs better with covariate values in this range), you will be fitting a linear constraint. With a little thought, you can probably see how to fit other functional forms (e.g. polynomial or logistic decay in the effect of distance on detection probability). You'll probably want to include a couple of functional forms in your model set.

My personal opinion is that you would be better off treating your distance categories as a continuous covariate, especially if your data set is not large. There is also no reason why you can't include both options in your model set and use model selection procedures to see which parameterization is better.

Brian