Difference between estimated and derived densities

[jnwaite]

I've been fitting a series of full-likelihood models using the groups option to model sex-specific differences in density, g0, and sigma. This results in separate density estimates for each sex, but I was also interested in the overall density, along with confidence intervals. I haven't been able to figure out how to get this information using the predict() function, so I attempted to use derived() without any sort of groups specification. I had expected the total density from derived() to be roughly the same as if I had added the sex-specific densities from predict(), but I got entirely different results. I also get entirely different (and contradictory) results if I DO specify groups in the derived() function.

So, my question is, how are the derived density estimates different from the predicted density estimates when using full likelihood models? Does it even make sense to use derived() in this fashion, even to get estimates of overall, group-combined densities with confidence intervals?

As an aside, I've also fit all my models using the conditional likelihood, and I get entirely different results in terms of which effects are important. For example, given the following two pairs of models:

Code: Select all

fit.sex.cl <- secr.fit(captHist, model=list(g0~sex, sigma~sex), CL=T)
fit.cl     <- secr.fit(captHist, model=list(g0~1,   sigma~1  ), CL=T)
fit.sex.fl <- secr.fit(captHist, model=list(g0~g,   sigma~g  ), CL=F, groups='sex')
fit.fl     <- secr.fit(captHist, model=list(g0~1,   sigma~1  ), CL=F, groups='sex')


Examining the AICc values for the conditional likelihood models indicates that the model with the sex effect is preferable over the constant model with quite a difference in AICc values. The opposite is true with the full likelihood models, with the sex effect model being substantially worse.

[murray.efford]

Hi

It's easy to trip up on these comparisons. We can't see the specifics of your problem, but in general:

derived() will give (almost) exactly the same estimates as a full likelihood model fit when the population is homogeneous. Otherwise, I suspect there is potential for divergence, but I would not have expected 'entirely different' results.

derived() computes animal-specific effective sampling areas a_i for the n detected animals and sums 1/a_i. The individual computations take into account any individual covariates (from a CL = T model) but not group membership (from a CL = F model). So I expect your attempts to use derived() in this case simply treated all animals as belonging to the first sex.

A good way to get a combined-sex density while fitting a sex-specific model is to use the hcov argument (see ?hcov for examples).

Your set of AICc comparisons assume 1:1 sex ratio for the full-likelihood models, which may be why the result differs.

Murray

[jnwaite]

Thank you for the reply. I've switched to hybrid mixture models and can now easily get both group-specific and combined density estimates.