Grouping Factors in a Robust Design

[brp]

We have been trapping foxes for the past 3 years. We have a robust design with 3 primary sessions (years: 2007, 2008, 2009) and 4 secondary occasions (days) within each year. I plan to use habitat type (4 levels: MDSR, MDSG, Gfine, Gclay) and distance to road (2 levels: near, far) as grouping factors, age as two states (pup and non-pup), and sex as a dummy covariate.

Is it true that each fox must be in exactly one group (combination of habitat and distance to road)? In other words, foxes observed in multiple habitats and/or distance to road categories throughout the 3 years must be excluded from the analysis?

We are not interested in transition probabilities between habitats or between distance to road categories. Therefore, I don't think we want to treat habitat or distance to road as multiple states.

[Bill Kendall]

First I would return to Murray Efford's question to you earlier. Is abundance or density your main interest? If it is, then the RD approach is not necessary. You have stated you are not interested in transitions. So is survival your main interest? If so, if you ignore the transitions between habitats and distance you will end up underestimating the differences in survival to some unknown extent.

I don't know how much data you have. I suspect your sample sizes are not huge, and you only have three years of data. Therefore, especially if the movements between those habitat and distance classes are minimal, ignoring them will likely end of being the best approach.

Howerver, in general, decisions about whether to include more state structure aren't based just on your interest in transitions. It is about the effect of undescribed heterogeneity in parameters, both nuisance (p) and demographic (S). MS models entail more parameters, but in some cases it is better to include the extra structure and sacrifice things like time variation, or include random effects, to get the number of parameters down. You can set up the more general structure and evaluate these issues with the data through model selection, or through simulation.

[brp]

My question from earlier:
Is it true that each fox must be in exactly one group (combination of habitat and distance to road)? In other words, foxes observed in multiple habitats and/or distance to road categories throughout the 3 years must be excluded from the analysis?

I'm assuming the answers to the above questions are YES and YES. Correct?

To answer your questions:
Our main interest is in survival.

We have 360 foxes captured at least once over the 3 years. I propose we exclude 44 foxes from the analysis for the following reasons.

18 were captured in 1 habitat but >1 road category.
14 were captured in 1 road category but >1 habitat.
12 were captured in >1 habitat and >1 road category.

Therefore, we have 316 foxes to use in our robust design analysis.

Would you consider 44 foxes out of 360 to be miminal? Would you suggest excluding the 44 foxes or adding habitat (4 categories) and road (2 categories) as additional states? Per your earlier suggestion, I think we will be using age (pup vs. non-pup) as two strata.