Issue with an error message when using the function intMsPGOcc() to do Occupancy with multiple data sources

[lnovo98]

Good evening, It's my first time using GitHub, sorry if I am not explaining my issue clearly enough.

I am currently trying to run a code using the intMsPGOcc() function from the spOccupancy() package to calculate occupancy values for mammal species from two different dataset: camera traps and foot survey

I already used the spatial function spMsPGOcc() in the past for the camera traps and it worked well !

However, this time using both camera traps and foot survey data it is not working anymore at a certain point. I followed the function description and coded my arguments the same way as the one provided in the spOccupancy package example. However, I keep getting the same error message: Error in chol.default(W) : the leading minor of order 59 is not positive definite

When only running the function with one chain it works fine, but as soon as I increase the chain to 2 or more the error message pops up.

Here is how my data and code look: Camera traps: 39 species for 183 sites with a repeat visit of 4 (=number of weeks cameras were active) Foot survey: 26 species for 136 transects with a repeat visit of 2 (=beginning and end of the month)

data.list <- list(y = y, a list of 2 objects containing respectively an array for the camera traps data source (39x183x4), and an array for the foot survey (26x136x2) occ.covs = mat.env, numerical matrix [1:319, 1:15], that contains the total of sites (cameras + transects) and the considered environmental covariates (15) that could be influencing occupancy and will be written in the formulas det.covs = det.covs.L, a list of two other lists (one for cameras, one for transects) that each contains the detection covariates as numerical vectors that we believe will influence the species detection, and as well will be included in the formula sites = sites.int, a list of 2 numerical vectors with the site number, one for cameras and one for transects species = species.int) a list of 2 character vectors that both contains the 39 species name for camera traps and the 26 species name for the transects

occ.formula.int <- ~ scaled_drivers_km Formula for occupancy, scaled_drivers_km = minimum distance in km of a site from the river, simplified for model trials det.formula.int = list(C = ~CtDays, Formula for camera (C) detection, CtDays = number of active days T = ~Gbs + Wo ) #Gbs + Wo) Formula for foot survey (T) detection, Gbs = proportion of open grassland, Wo = proportion of open woodland

prior.list <- list(beta.comm.normal = list(mean = 0,var = 2.73), alpha.comm.normal = list(mean = list(0, 0), var = list(2.72, 2.72)), tau.sq.beta.ig = list(a = 0.1, b = 0.1), tau.sq.alpha.ig = list(a = list(0.1, 0.1), b = list(0.1, 0.1)))

inits.list <- list(alpha.comm = list(0,0), beta.comm = 0, alpha = list(0, 0), beta = 0, tau.sq.beta = 1, z = matrix(1,46,J), J = 319, number of total sites fix = T)

outputs <- intMsPGOcc(occ.formula = occ.formula.int, det.formula = det.formula.int, inits = inits.list, priors = prior.list, data = data.list, n.samples = 1000, n.omp.threads = 1, verbose = TRUE, n.report = 10, n.burn = 100, n.thin = 30, n.chains = 2)

summary(outputs, level = 'community')

I already tried multiple combinations with the number of sample, burn and thinning but the error message keeps happening

outputs <- intMsPGOcc(occ.formula = occ.formula.int,

• det.formula = det.formula.int,
• inits = inits.list,
• priors = prior.list,
• data = data.list,
• n.samples = 1000,
• n.omp.threads = 1,
• verbose = TRUE,
• n.report = 10,
• n.burn = 100,
• n.thin = 30,

• n.chains = 2)

  Preparing to run the model

  tau.sq.beta is not specified in initial values. Setting initial values to random values between 0.5 and 10

Fixing initial values across all chains

---

Model description

---

Integrated Multispecies Occupancy Model with Polya-Gamma latent variable fit with 319 sites and 46 species. I believe 46 species are the common species between the 39 detected with camera traps and the 26 species detected with transects

Integrating 2 occupancy data sets.

Samples per Chain: 1000 Burn-in: 100 Thinning Rate: 30 Number of Chains: 2 Total Posterior Samples: 60

Source compiled with OpenMP support and model fit using 1 thread(s).

---

Chain 1

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Sampled: 1000 of 1000, 100.00% Error in chol.default(W) : the leading minor of order 61 is not positive definite

[doserjef]

Hello!

Thanks for the background information on your data sets, and sorry to hear you're running into this problem. That error that you are getting happens when there is a problem when calculating the Rhat (Gelman-Rubin diagnostic). This is only done when running with multiple chains, which explains why you're not seeing the problem with a single chain. Usually this occurs because there is some parameter in the model that is not being estimated properly, which could arise from a bad initial value (although the ones you supply seem fine), a problem with the data formatting, or some specific case with a given data set (i.e., extremely rare species). Could you send me your data set and script via email (doserjef@msu.edu) and I can take a look at it?

Thanks,

Jeff

[lnovo98]

Hi Jeff ! Thank you so much for your reply, I am sending you my script and dataset.

Have a good day,

Cheers,

Lucy

[doserjef]

We figured out this error was occurring because the burn-in period was not long enough, and some very large values at the beginning of the MCMC chains were leading to an error when intMsPGOcc() tries to calculate Rhat. Running the chains for longer with a longer burn-in eliminated the error.