AI-GEOSTATS: Cokriging wildlife density
- Dear Ai-Geostats members:
I'm new to this list in the sense that I never posted a message, but I followed all your discussions in the last year, and I think many of you could help me.
I'm a wildlife biologist, trying to use geostatistics to assess density of a roe deer (capriolo, cabirol, chevreuil, rehwild...) population. In doing this, i have to face many theoretical problems I usually am not able to solve.
I explain you briefly the procedure I'm attempting to use to ask then my questions:
I gather point density estimates (the primary variable) by mark-resight. I do this for several years, and putting time on the z axis, I estimate my variograms and cross-variograms with other variables. I obtain predictions by ordinary cokriging. I cross-validate my results, just for the primary variable.
1) I'haven't primary variables measures, I have estimates. It was suggested me to use a variogram model to study spatial dependence that could be different by zero for lag=0, as of course in such a situation an exact interpolator could not be the best solution. But how could I use such a model in a linear model of coregionalization? My covariates are measured, not estimated.
Is it better to use my estimates as measures (so using a classic variogram = 0 for lag=0) or to discard the linear model of coregionalization, estimating my error variance by cross-validating results?
2) the sill of my variograms are equal or larger than primary variable variance (so, more or less twice the semivariance). It is probably because of a trend in the density, that decreased with time. The primary variable (deer density) is probably a second order stationary one, at least for a much larger area than my study area, being the last surrounded by many kilometers of deer suitable habitat. But it behaves like non stationary in the few square kilometers of interest and in the few years of sampling. May I ignore this problem or do I have to incorporate the trend?
3) when I cross-validate my predictions (obtained with linear model of coregionalization and ordinary cokriging) I obtain enough good results. But I argue that perhaps they are even better than it could seem. Not only because of problems of all cross-validations, but because I have to compare my predictions not with actual measures, but with estimates. Probably the average error is influenced by both uncertainties. Given that I know the confidence intervals of my primary variable estimates, how could I account for them to estimate correctly the average error of my prediction model?
Hoping to have been enough fair (your fascinating language is very hard for a poor biologist), I thank all of you for any help (direct or bibliographic) I'll receive.
I take this opportunity to send my best regards to Edzer, that already helped me to go on in this work and whose software I'm still using, without problems of any kind.
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