I am only estimating p, which is a function of up to several individual covariates that vary over time and among capture histories. One of those individual covariates is 'Date of visit' treated as a continuous variable. There is no categorical visit effect.
Numerous missing observations are present. Perhaps on average > 75% of a given capture history is a missing observation.
I analyzed some simple fake data sets and found that missing observations can have a large impact on the estimated detection probabilities (and thus presumably on abundance). I am wondering whether I should be concerned by this and, if so, what, if anything, I can do about it. I tried conditioning the data by deleting all visits in a given capture history up to and including the first detection. That helped with some fake data sets, but not when the pattern of missing observations became complex.
My understanding is that the Huggins design was developed to estimate abundance of a closed population when individual animals were physically captured and recaptured. Under this scenario I am unsure how a missing observation would even arise, unless an animal was not released on its last capture.
Temporary emigration might allow for an animal not being present on a given visit, but in that case I would think the animal would be recorded as a 0 instead of a missing observation.
I also have been getting a warning message that I cannot locate in the MARK documentation or on the internet:
* * WARNING * * One or more encounter histories have probabilities not in interval 0-1.
If I repeatedly analyze the same subset of data using the same model then maybe 75% of the model output files will not contain the warning and 25% of the model output files will contain the warning. Parameter estimates will vary regardless of whether the warning is present. This suggests to me that numerous local maxima are being found.
I tried to calculate out the probabilities for each capture history when the warning was present, just for visits without missing observations, and the values ranged from 1.514228e-08 to 4.600842e-01. These numbers would be smaller if I included p's for visits with missing observations, but I do not think they would go below zero.
Perhaps this warning arises if the probability of being captured at least once is so small that MARK thinks it is effectively zero and then, from page 14-5 of the MARK book, tries to divide by zero? But I do not see how that is possible either because p for a given site on a given visit seems to stay above 0.25.
Thank you for any thought regarding how to deal with 75% or more of a data set being a missing observation when using the Huggins design (or whether I should even be concerned about it) and for any thoughts regarding the above warning message that MARK returns.
Perhaps I should state that individual rows in the data set are not individual animals, but rather individual areas.