Hi all,
I am using RDOccupEG (robust-design/multi-season occupancy) in RMark to estimate within-season site occupancy dynamics of a rare and highly mobile grassland bird. Our field crew conducted >10,000 repeat-visit surveys at >1,000 sites during two breeding seasons. We have very sparse data for this particular species (approximately 130 detections at 100 sites across the entire study). The RD approach has worked quite well, but I am running into a problem that I'm not sure how to address...
One of my individual covariates is a simple categorical factor for seasonal Fire (Burned versus Not Burned). Prescribed prairie fires occur during late winter/early spring here. This species requires tall, dense vegetation for nesting and WILL NOT use burned sites during the early breeding season, but will use burned sites later in the season in areas that are not grazed by cattle, where vegetation grows rather quickly. I have been able to capture this pattern: based on multimodel selection, Fire is an important predictor of initial site occupancy (Psi), but not an important predictor of within-season site colonization (Gamma). The effects on Psi are apparent when I plot the data -- Psi increases linearly with % Unburned Grassland Cover as one might expect, whereas Psi is a flat line at 0.0 across the entire range of % Burned Grassland Cover (doesn't matter how much grass there is; if it's burned, Psi = 0.0). So, that's cool.
However, this estimate of Psi = 0.0 is at the parameter boundary, so standard errors for beta estimates are also 0.0. My beta estimates for Psi in the top model are as follows:
Intercept (Burned): beta-hat = -19.95, SE = 0.0 (95% CL = -19.95, -19.95)
Fire (Unburned): beta-hat = 14.47, SE = 0.0 (95% CL = 14.47, 14.47)
% Grassland: beta-hat = 1.28, SE = 0.36 (95% CL = 0.58, 1.98)
% Conservation Reserve Program: beta-hat = 0.57, SE = 0.12 (95% CL = 0.33, 0.81)
% Trees: beta-hat = -0.90, SE = 0.50 (95% CL = -1.88, 0.09)
All estimates are on the logit scale and based on z-transformed covariates. This model provides the single-best fit among my candidate set for Psi, and a plot of the data looks good (again, flat line at 0.0 for burned grass, and a positive effect of unburned grass with fairly tight confidence intervals).
My question: Is the standard error equal to 0.0 for the intercept and Fire a problem? As I understand it, if the parameter is at a parameter but is estimable, then it's okay to ignore the SE = 0. It makes sense -- birds never use burned sites early in the year. But unfortunately this also leads to SE = 0 for the unburned parameter as well? Is it appropriate to retain these effects and present the beta estimates as they are, or would you suggest removing this as a candidate effect in the analysis, and simply provide information on detections at burned versus unburned sites throughout the season as descriptive statistics (i.e., "we encountered zero birds at burned sites during the early season, but found x birds at x burned sites later in the year"...)?
I'd like to retain this effect, but don't want to raise any red flags when I submit these results for publication. I'd appreciate any opinions about this - thanks!!
Best,
Mark