Correlated detections- numerical convergence error

questions concerning analysis/theory using program PRESENCE

Correlated detections- numerical convergence error

Hello all, I am carrying out a survey to understand human-wolf interactions in a human dominated landscape in the state of West Bengal, India. The project has two stages- first being the estimation of habitat use of the wolves in the study area (with which I am facing the problem) and second are interviews.

The work:

The first stage of the project is to understand the wolf habitat-use in the area. The study area is relatively small ~200 sq kms. For this, the grid size thus was selected to be of 4 sq kms (2km by 2km). A total of 44 grids were surveyed, with survey tracks ranging from 1 to 6 kms. Now, owing to logistic, time and other fieldwork related constraints I have used spatially replicated sign surveys. I collected the sign data for every 250m segments and later aggregated it to 1km segments. I am also using 7 covariates for psi according to the ecology of wolves and 2 covariates for detection probability. Out of the total 44 surveyed grids 15 sites were occupied (grids with at least one sign of wolves). I am very new to occupancy analysis and having difficulty going through the process.

The issue:

While analyzing the data on PRESENCE using correlated detections model, whenever I am running models, I get warnings of 'numerical convergence not reached'. Now, for most models the significant digits are more than 3 or 4 and sometimes more than 5. However, whenever I put more than two covariates to run a model for psi, the significant digits drop down to 1 and the standard errors increase by manifolds or go into negative SE! The habitat use probability of individual sites also show just 1 and 0s. Additionally, I am very confused with the th0pi() parameter.

Could my issue be because of less detection data and thus not much variation in the data? Could the issue be related to the design matrix? Can I use single covariates to model habitat use? What would be the proper way ahead?

I can provide additional information if needed for clarification.

Thanks,
Aakash
aakashbhushan

Posts: 4
Joined: Thu Mar 16, 2023 5:32 am

Re: Correlated detections- numerical convergence error

Hi Aakash
Check out the FAQ for some suggestions that might be useful viewtopic.php?f=40&t=665
Cheers
Darryl
darryl

Posts: 493
Joined: Thu Jun 12, 2003 3:04 pm
Location: Dunedin, New Zealand

Re: Correlated detections- numerical convergence error

Dear Darryl,
However, the problem still persists. When I add more than two covariates to a model, it gives dubious results.

I think the issue is with the sample size. I have only 44 sites and of them, only 15 with detections. Maybe that's why adding too many covariates is creating a problem.

Additionally, the th0pi() parameter is very confusing for me. Keeping it at '1' gives different estimates, keeping it at '0' gives something else and when fixing it to EQ give some other estimates.

Regards,
Aakash
aakashbhushan

Posts: 4
Joined: Thu Mar 16, 2023 5:32 am

Re: Correlated detections- numerical convergence error

It does sound like you're trying to include too many covariates so the model is overfitting the data and some parameters may not be fully estimable (indicated by the negative SEs).

With that sample size I think you don't want to be estimating any more than 2-3 occupancy-related parameters (how many covariates that translates to depends whether you have continuous or categorical valued covariates), and maybe 3-4 detection-related parameters.

From looking at the data, does it look like you have correlated detections (ie you have pulses of consecutive 1's and consecutive 0's)? If not, you can also try the regular single season model which has a simpler detection process.
darryl

Posts: 493
Joined: Thu Jun 12, 2003 3:04 pm
Location: Dunedin, New Zealand

Re: Correlated detections- numerical convergence error

Dear Darryl,
The data for the grids with wolf detections look like this:
Grid Rep1 Rep2 Rep3 Rep4 Rep5 Rep6
9 0 1 - - - -
10 1 0 - - - -
17 0 1 1 - - -
19 1 1 0 - - -
22 1 0 0 - - -
25 0 1 - - - -
26 1 0 0 0 0 -
27 1 1 0 0 - -
29 0 1 0 0 0 -
34 1 0 0 0 - -
43 0 1 0 0 0 0
and so on...
It looks like the data has correlated detections...?

My site covariates are continuous. As per the suggestion, I will run models with less covariates. Maybe 1 or 2 at max and see the estimates.

Regards,
Aakash
aakashbhushan

Posts: 4
Joined: Thu Mar 16, 2023 5:32 am

Re: Correlated detections- numerical convergence error

Dear Aakash,

In general, Darryl's suggestion of a max of 2-3 covariates for occupancy and 3-4 for detection covariates in a model makes perfect sense. In practice, the max number of covariates will also depend on the data.

From the sample of data you included in your post, it appears that nearly all sites have detections. If the rest of the sites are like this, then naïve occupancy will be nearly 100%. When occupancy is very high, there isn't much possibility for occupancy to vary in the presence of a covariate. If occupancy is 100%, then the standard error of psi will be undefined and you will likely see error or warning messages about convergence and/or problems with the variance-covariance matrix.

Also, the correlated detections model adds new parameters to the standard model, which may reduce the number of covariate-effect parameters you can estimate. I recommend that you start with the simplest model (no covariates) and try adding covariates one by one until you see problems.

Cheers,

Jim
jhines

Posts: 587
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA

Re: Correlated detections- numerical convergence error

Dear Jim,

The sample data that I shared is only for the sites that has detection. As I mentioned on my first post, out of 44 site that were surveyed, I have only 16 sites with detections (at least one detection per site). This sample data is from those 16 sites.

I shared the sample data since Darryl suggested to check if I have consecutive 1s and 0s. Apologies for the confusion.

As per Darryl's suggestion, I ran models using simple single season model and that gives acceptable results.

Regards,
Aakash
aakashbhushan

Posts: 4
Joined: Thu Mar 16, 2023 5:32 am