by **JDJC** » Wed Jul 29, 2015 9:32 am

Just to quickly chime in:

The estimates of density from the package 'secr' are not Poisson random variables: these (the number of activity centers and their locations) are marginalized out of the likelihood, and the output parameter D-hat is more like the average of a Poisson spatial point process...so more like a lambda than a y1, y2, etc. If using a Bayesian approach, you retain the latent activity center variables, but the posterior distribution is not likely to be an integer either.

At any rate, I think most people would argue that it is more robust to model variation in density within the SCR or SECR model itself (in the same way that you are better off modeling variation in survival directly within a CJS model rather than running regressions on the parameter estimates afterwards). The issue (as I vaguely understand it) is that running stats on stats fails to properly account for variance: each d-hat has a standard error that is related to detection parameters with a standard error, and running an unweighted regression on d-hat post-hoc is not really accounting for the variance in the estimate itself. In other words, treating a parameter with some error value like a perfectly observed data point. Which I guess you could get around if you used some sort of weighted glmm, if this sort of thing exists. But an additional reason to consider variation in the state parameter within a scr or c-r model is that it may influence estimation within the nested detection model as well.

It is not terribly difficult within the 'secr' package (Murray has written a vignette on doing so), and you are fully capable of considering group, session, or spatial covariates within the linear predictor (log-link, identity link, spline).