Large SEs and h2 models

[jcl...@utk.edu]

I am running some models for density estimation for female black bears based on DNA sampling and my top model is:

D ~ session + p_for ,  g0 ~ bk + h2, sigma ~ bk + h2, where p_for is a density surface covariate (percent forest).  

The model converges okay but these are my beta estimates:

                                 beta      SE.beta                 lcl                   ucl

D                   -27.5916799  3.94217131  -35.3181937   -19.8651661

D.session2    -0.7066832   0.23189244  -1.1611840  -0.2521824

D.p_for          22.0948167   3.97872999  14.2966492  29.8929842

g0                    -1.5428311   0.24975504  -2.0323420  -1.0533203

g0.bk                1.8027544   0.26653832   1.2803489   2.3251599

g0.h22             -2.7485302   0.18378184  -3.1087360  -2.3883244

sigma               6.7902722   0.09227502   6.6094165   6.9711279

sigma.bk          5.6755250   43.76648404 -80.1052075  91.4562574

sigma.h22        1.2994172   0.12515557   1.0541168   1.5447176

pmix.h22          0.2117920    0.34604190  -0.4664377   0.8900217

Should I be concerned about the large SEs for sigma.bk and pmix.h22?  I know about the problems with estimation for h2 models but the estimates without the h2 parameter are obviously low.  The estimates for the above model are reasonable and I have used different starting values and cannot find any obvious problems with multimodality.  Thanks!

Joe

[Eric H]

Good day,

One possible reason for the large SE on the pmix parameter is that, as I understand it, the h2 models divide individuals into the same 2 groups/mixtures for both g0 and sigma (animals with higher g0 are the same ones that have higher or lower sigma). If animals don't fall into the same groupings according to g0 and sigma, this model might not fit well(?). If animals of both sexes are included in the data, the difference in sigma between sexes might make it hard to discern differences in g0 between any grouping of animals other than sexes. Then, if g0 varied with age or across sessions, it would become difficult (imprecise) to assign animals to groups. All speculative.

Regarding the bk effect. We sometimes see support for a sex*bk interaction on g0. I've never been able to wrap my head around what a location-specific learned response on sigma means with respect to bear behaviour (animals travel farther from their activity center to revisit the same trap, but not to find other traps). Did you try a general learned response on sigma in combination with a bk effect on g0? Also, depending on the timing of sampling, home range size and therefore sigma might increase over time independently of exposure to traps. Not sure if this might create a pattern in the data that would lead to support for a positive trap response on sigma. Even more speculative.

I might look at parameter estimates from simpler models (e.g. removing one effect at a time) to see if they yield more precise estimates of some of these parameters. I can't make a recommendation about which model(s) to draw inference from, as I'm constantly struggling with similar issues in our own data.

Eric

[jcl...@utk.edu]

Thanks for the insight Eric, I was hoping you would chime in as I know you have thought a lot about this.  All these estimates are for females so a sex effect doesn't enter into it.  I have run models without the H2 covariate on either g0 or sigma, and they converge, sometimes with more precise estimates of h2 and pmix, but the AIC is much higher.  I am running a model for session 1 by itself, and it seems to be converging on similar estimates of D.  I guess what I am asking is do the high SEs for sigma.bk and pmix.h22 warrant throwing out those models?  It took a long time for this model to converge (it ran out of iterations the first time so I had to restart it with more iterations) but it finally did with no errors or warning messages.

[Eric H]

Hi Joe,

I don't have a simple answer, and I haven't found many strong recommendations regarding when h2 models should be used vs. mistrusted. SEs larger than point estimates seems a defensible reason, but I'm not sure it means you should throw them out. Articles by Pledger suggest that we need a minimum of 6 occasions with CR data, but I'm not sure how that translates to proximity or count detectors. 

We know that when data are sparse, h2 models either aren't supported, or can yield implausible parameter estimates. When data are very rich, models with h2 yield the similar or slightly higher point estimates as models that ignore it, but with larger SEs. Most real data sets fall somewhere in between, where h2 models yield estimates that might be more accurate, but are also potentially unrealiable and misleading and may be too imprecise to be useful. AICc doesn't seem to be enough to discern these differences. Right?

If I see small (e.g. < 20%? < 30%?) differences in Dhat between models with and without h2, I might assume that the h2 effect is "doing it's job", and not look much further. If adding h2 to a model e.g .doubles the density estimate, I get suspicious. The estimate from the model without h2 is almost guaranteed to underestimate, but the point estimate from the h2 model might not be meaningful, and the SE is large, so which is more useful? 

I sometimes use predict(all.levels = T) to see if the parameter estimates for both mixtures on the real scale make sense. If I see difference > e.g. an order of magnitude in g0 or sigma within sexes I might call that "implausible" and throw the model out. Same if I see a very small fraction of the population with very low detectability leading to a high and imprecise density estimate (as often happens when the data include more than a few single captures), or if some combination of bk and h2 lead to the inference that initial g0 for some non-negligible number of bears close to 0. 

Again, more words than real help.

Eric