HUGE coefficient standard error values

[jasonmartin13]

I'm running occupancy models and I'm getting huge values (think 11+ digits) for the beta standard error estimates, even when no covariates are included. Model fit seems to be fine. Does anyone have any thoughts about what might be going on? Something to do with distribution of capture histories perhaps? If this is the problem, what kind of mimimum distribution of capture histories might be necessary to produce accurate estimates?

My capture histories are as follows:

History #observed
010 10
001 14
000 33
110 3
011 3
111 1
100 6
101 2

Thanks!

Jason

[jhines]

Jason,

When a parameter is near the boundary, the untransformed beta estimate is either very large positive or very large negative if you're using the logit link function. When this happens, it takes a fairly large change in the beta in order to have any effect on the real parameter. That's what the large standard error is telling you.

In practice, you might say the standard error of that real parameter estimate is undefined, zero, or inestimable. The good news is that the standard error of detection is usually OK when this happens.

If you get very large standard errors when the estimate is not near a boundary (zero or one), then you probably have an overparameterized model (too many parameters and/or not enough data).

Cheers,

Jim

[throop]

You mention that the standard error of detection is usually ok when this happens. Why is that, and what if it happens for occupancy covariate betas? Also, how large are we talking about? I have seen SE with 7 place values (1123165), but I have also seen SE estimates of 8.something.

I also wanted to ask about inclusion of an over-parameterized global model. For a global model, which variables are necessary for inclusion? With 50 site variables and 8 survey variables, A global model including all would be far over-parameterized.

Finally, how would you interpret the SE for the detection intercept crossing 0?

Thanks for your help!

[dhewitt]

If your real parameter estimates are 0.9999 or 1.0 (or 0) and the SEs are 0 or 1 (or real close), your estimate is on a boundary and you've got one of two situations:

(1) parameter really is 0 or 1

or

(2) you dont have enough data to estimate the parameter.

You can't necessarily decide which is the case.

If the data set you provided is the whole thing, you can't chase anywhere near 50 covariates on Psi and 8 on p. That's not YOUR global model. One or two is probably it, but for some reason MARK is bombing on my machine right now and I can't check.

[dhewitt]

You mention that the standard error of detection is usually ok when this happens. Why is that, and what if it happens for occupancy covariate betas? Also, how large are we talking about? I have seen SE with 7 place values (1123165), but I have also seen SE estimates of 8.something.

As a follow-up on this, I just ran your data via RMark with a dot model on p and a time-dependent p, both with a dot model on Psi (duh).

I am curious about your results and I hope Jim/Jim/Darryl/etc. might comment. The p's are decent but the Psi boundaries at 1. Given that about half your histories are '000' I am confused as to why this occurs (this relates to your original question about 'distribution of capture histories').

From the output below you can see what Jim meant about p being OK even when Psi boundaries. The SEs are good on p, even when a separate one is estimated for each survey.

[[1]] p(~1)Psi(~1)
-2lnL: 231.3119
AICc : 235.4859 (unadjusted=233.36909)

Real Parameter p
0.2269 (se=0.0285) CI=(0.176, 0.287)

Real Parameter Psi
Psi 1 (se=0) CI=(1, 1)


[[2]] p(~time)Psi(~1)
-2lnL: 228.6661
AICc : 237.2631 (unadjusted=235.01906)

Real Parameter p
p1 0.167 (se=0.0439) CI=(0.097, 0.271)
p2 0.236 (se=0.05) CI=(0.152, 0.347)
p3 0.278 (se=0.053) CI=(0.187, 0.392)

Real Parameter Psi
Psi 0.9999997 (se=0.0010864) CI=(0, 1)


- Dave Hewitt

[jhines]

Dave,

I'm not sure what your follow-up question is.

If psi=1, and p=.2268, then the probability of the 000 history is:

1-(1-p)*(1-p)*(1-p) = 0.4621555

The expected number of sites with this history is:

72*0.4621555 = 33.275192

The observed number of 000 sites is 33.

Jim

[darryl]

Any reason why psi could not be near 1 for this species?

Note that if p really is that low, then 3 surveys are insufficient to give a good estimate of occupancy and that really you should be doing many more. The real key to getting a good estimate of occupancy isn't only taking account of detection probability, it's about getting good data in the first place, even if that means going to fewer places.

Darryl

[dhewitt]

Jim and Darryl,

I was surprised that Psi would be 1 with that many '000' histories. I stand corrected.

- Dave

[dhewitt]

Posting for Marc Kery (Swiss Ornithological Inst):

"I think that there may be an alternative explanation: small sample bias of the site-occupancy estimates. It is known right from the 2002 publication by Darryl et al that p may be under- and psi overestimated in small-sample situations. That is, when the number of sites or the number of surveys or p is small. So, in addition perhaps to what Darryl just explained, it may be that your occupancy estimate is biased high. You seem to have only three surveys, and with small p, your psi estimate can go soaring. This is rather easily checked using simulation."

I'd say the conclusion is that the data set presented is simply too sparse to obtain a reliable estimate of occupancy. Visit fewer sites more times and search hard!