Very large values for ‘nu’ in 2-species co-occurrence model

[lkwander]

Hello –
Wanted to start by saying thanks so much for creating this support resource – it’s been extremely helpful as I navigate learning to apply these modeling tools.

I’m trying to do very simple 2-species co-occurrence model sets to test independence of occupancy and detection, using the multi-season model for my 2 years of sampling. I’m using the nu/rho parameterization.

My first question is that while I’ve found explicit definitions for ‘nu’ online (odds ratio of the SIF for occupancy) I haven’t been able to find that for ‘rho’ – it is the odds ratio of the SIF for detection, right?

Secondly, I’m getting some extremely large values for nu in my results (e.g., 12-22 digits). As far as I understand it’s unbounded so theoretically ok, but it seems like it is an indication that something is off. I am also getting standard errors of ’10’ in my results (see below), also indicating something isn’t correct. Any recommendations?
estimate std.error
A1 psiA : 83.512983 1.060879
A2 psiBa : -82.950290 1.060798
A3 nu : 0.546662 10.000000
D1 pA[1] : -3.231477 0.511750
D2 pB[1] : -0.010726 10.000000
D3 rA[1] : -1.114663 0.107193
D4 rBa[1] : -3.017265 0.249219
D5 rho[1] : -1.169320 0.751430

By the way, the data are 22 sites with 10-20 surveys in each of the two years. One species is fairly abundant, but the other is more rare - with only 10 detections in the first year and 11 in the second.

Thanks,

Lauren

[darryl]

rho has similar interpretation as nu, but for detection. ie odds ratio for how the probability of detection changes if the other species is detected in the same survey.

Difficult to interpret the coefficients without the design matrix, but SE's of exactly 10 is suspicious. Any warnings included in the output?

Darryl

[lkwander]

No - no warnings. Is there any way to upload or share the output file as it might give more clues?

Thanks,

Lauren

[jhines]

Hi Lauren,

Do you have detections of species A at every site? Your estimate of psiA is 1.0, so the psiBa cannot be computed as there are no possible sites where species A is not there. That makes the concept of SIF irrelevant.

Jim

[lkwander]

Hi Jim,

Thanks for your reply - species A isn't at every site, but almost (0.90=naive). Plus there are a lot of surveys (many 0s) so detection is low.

I tried to simplify things by using a different species A (one with occupancy around 0.65) and for only one season, but am still getting similar types of errors:

estimate std.error
A1 psiA : 0.555359 0.557732
A2 psiBa : -25.825026 3.974541
A3 nu : 26.189883 3.974364
B1 pA[1] : -1.516657 0.345318
B2 pB[1] : -0.114702 10.000000
B3 rA[1] : -2.974566 0.402206
B4 rBa[1] : -2.611166 0.435951
B5 rho[1] : -0.110034 10.000000

I also tried collapsing survey transects (from 30 to 6) with not appreciably different results:

estimate std.error
A1 psiA : 0.696875 0.642816
A2 psiBa : -44.879470 2.305345
A3 nu : 45.383782 2.305259
B1 pA[1] : 0.576975 0.628885
B2 pB[1] : -767.870967 10.000000
B3 rA[1] : -1.341830 0.509577
B4 rBa[1] : -1.142031 0.573888
B5 rho[1] : 0.477477 0.580132

Any ideas are appreciated!

Thanks,

[jhines]

Hi Lauren,

I don't think posting the output (other than what you've already posted) will give much more info for diagnoses. If I could see the input, I might be able to tell what's going on. If you don't want to post it here, you can email it to me (jhines@usgs.gov).

Cheers,

Jim

[lkwander]

Just to complete this thread for anyone else experiencing these types of issues, this was the final diagnosis and outcome for this dataset/analysis:

There were a lot of surveys (60, 30 in each season) but only 22 sites, so occupancy, colonization and detection will be very poorly estimated. Plus Jim pointed out that the 2-species models have a lots of parameters to estimate.

Jim suggested using the conditional parameterization (psiA,psiBA,psiBa,...) instead of the the odds-ratio parameterization as the conditional one performs better with sparse data.

I ran the simplest model possible that Jim outlined: parameters were different for species A and B, but not dependent on each other: psiA, psiBA=psiBa, gamA, gamBA=gamBa, epsA, epsBA=epsBa, pA=rA, pB=rBA=rBa (8 parameters). Then ran the model where detection is different when both species are present, versus when only one species is present (pA not = rA, pB not = rBA).

It definitely helped with convergence, but I still got some parameter estimates and standard errors that didn't seem "right" (parameters of zero and/or standard errors of exactly "10") so unfortunately I think I just don't have enough data for this analysis. Running the two years of data as separate, single-seasons (so no colonization and extinction parameters) didn't make much difference in terms of parameter estimates and standard errors that looked off.

Thanks to Darryl and Jim for helping me reach a conclusion at least!

Lauren