spOccupancy fits single species, multispecies, and integrated spatial occupancy models using Markov Chain Monte Carlo (MCMC). Models are fit using Polya-Gamma data augmentation. Spatial models are fit using either Gaussian processes or Nearest Neighbor Gaussian Processes (NNGP) for large spatial datasets. Provides functionality for data integration of multiple single species occupancy data sets using a joint likelihood framework.

Installation

You can install the released version of spOccupancy from CRAN with:

install.packages("spOccupancy")

Functionality

spOccupancy Function Description
PGOcc Single species occupancy model
spPGOcc Single species spatial occupancy model
intPGOcc Single species occupancy model with multiple data sources
spIntPGOcc Single species spatial occupancy model with multiple data sources
msPGOcc Multispecies occupancy model
spMsPGOcc Multispecies spatial occupancy model
ppcOcc Posterior predictive check using Bayesian p-values
waicOcc Compute Widely Applicable Information Criterion
simOcc Simulate single species occupancy data
simMsOcc Simulate multispecies occupancy data
simIntOcc Simulate single species occupancy data from multiple data sources

Example usage

Load package and data

To get started with spOccupancy we load the package and an example data set. We use data on twelve foliage-gleaning birds from the Hubbard Brook Experimental Forest, which is available in the spOccupancy package as the hbef2015 object. Here we will only work with one bird species, the Black-throated Blue Warbler (BTBW), and so we subset the hbef2015 object to only include this species.

library(spOccupancy)
data(hbef2015)
sp.names <- dimnames(hbef2015$y)[[1]]
btbwHBEF <- hbef2015
btbwHBEF$y <- btbwHBEF$y[sp.names == "BTBW", , ]

Fit a spatial occupancy model using spPGOcc()

Below we fit a single species spatial occupancy model to the BTBW data using a Nearest Neighbor Gaussian Process. We use the default priors and initial values for the occurrence (beta) and regression (alpha) coefficients, the spatial variance (sigma.sq), the spatial range parameter (phi), the spatial random effects (w), and the latent occurrence values (z). We assume occurrence is a function of linear and quadratic elevation along with a spatial random intercept. We model detection as a function of linear and quadratic day of survey and linear time of day the survey occurred.

# Specify model formulas
btbw.occ.formula <- ~ scale(Elevation) + I(scale(Elevation)^2)
btbw.det.formula <- ~ scale(day) + scale(tod) + I(scale(day)^2)

We run the model using an Adaptive MCMC sampler with a target acceptance rate of 0.43. We run the model for 5000 iterations split into 200 batches each of length 25. We discard the first 2000 iterations as burn-in and use a thinning rate of 3 for a resulting 1000 samples from the joint posterior. We fit the model using 5 nearest neighbors and an exponential correlation function. We also specify the k.fold argument to perform 2-fold cross-validation after fitting the full model.

# Run the model
out <- spPGOcc(occ.formula = btbw.occ.formula,
               det.formula = btbw.det.formula,
               data = btbwHBEF, n.batch = 200, batch.length = 25,
               accept.rate = 0.43, cov.model = "exponential", 
               NNGP = TRUE, n.neighbors = 5, n.burn = 2000, 
               n.thin = 3, verbose = FALSE, k.fold = 2)
summary(out)
#> 
#> Call:
#> spPGOcc(occ.formula = btbw.occ.formula, det.formula = btbw.det.formula, 
#>     data = btbwHBEF, cov.model = "exponential", NNGP = TRUE, 
#>     n.neighbors = 5, n.batch = 200, batch.length = 25, accept.rate = 0.43, 
#>     verbose = FALSE, n.burn = 2000, n.thin = 3, k.fold = 2)
#> 
#> Chain Information:
#> Total samples: 5000
#> Burn-in: 2000
#> Thin: 3
#> Total Posterior Samples: 1000
#> 
#> Occurrence: 
#>                          2.5%     25%     50%     75%   97.5%
#> (Intercept)            3.1509  3.7926  4.1715  4.6249  5.5584
#> scale(Elevation)      -0.9964 -0.6809 -0.5459 -0.4037 -0.1343
#> I(scale(Elevation)^2) -1.6453 -1.3531 -1.2003 -1.0468 -0.8206
#> 
#> Detection: 
#>                    2.5%     25%     50%     75%  97.5%
#> (Intercept)      0.4482  0.5918  0.6663  0.7413 0.8903
#> scale(day)       0.1551  0.2435  0.2942  0.3421 0.4333
#> scale(tod)      -0.1769 -0.0854 -0.0365  0.0138 0.1002
#> I(scale(day)^2) -0.2439 -0.1327 -0.0761 -0.0179 0.0784
#> 
#> Covariance: 
#>            2.5%    25%    50%    75%  97.5%
#> sigma.sq 0.4453 0.9454 1.4531 2.3372 4.6473
#> phi      0.0025 0.0046 0.0080 0.0147 0.0262

Posterior predictive check

The function ppcOcc performs a posterior predictive check on the resulting list from the call to spPGOcc. For binary data, we first need to perform Goodness of Fit assessments on some binned form of the data rather than the raw binary data. Below we perform a posterior predictive check on the data grouped by site with a Freeman-Tukey fit statistic, and use the summary function to summarize the check with a Bayesian p-value.

ppc.out <- ppcOcc(out, fit.stat = 'freeman-tukey', group = 1)
summary(ppc.out)
#> 
#> Call:
#> ppcOcc(object = out, fit.stat = "freeman-tukey", group = 1)
#> 
#> Chain Information:
#> Total samples: 5000
#> Burn-in: 2000
#> Thin: 3
#> Total Posterior Samples: 1000
#> 
#> Bayesian p-value:  0.423 
#> Fit statistic:  freeman-tukey

Model selection using WAIC and k-fold cross-validation

The waicOcc function computes the Widely Applicable Information Criterion (WAIC) for use in model selection and assessment.

waicOcc(out)
#>       elpd         pD       WAIC 
#> -673.44978   29.01647 1404.93250

Alternatively, we can perform k-fold cross-validation directly in our call to spPGOcc using the k.fold argument and compare models using a deviance scoring rule. We fit the model with k.fold = 2 and so below we access the devaince scoring rule from the 2-fold cross-validation.

out$k.fold.deviance
#> [1] 1503.163

Prediction

Out-of-sample prediction is possible using the predict function, a set of occurrence covariates at the new locations, and the spatial coordinates of the new locations. The object hbefElev contains elevation data across the entire Hubbard Brook Experimental Forest. Below we predict BTBW occurrence across the forest, which are stored in the out.pred object.

# First standardize elevation using mean and sd from fitted model
elev.pred <- (hbefElev$val - mean(btbwHBEF$occ.covs[, 1])) / sd(btbwHBEF$occ.covs[, 1])
coords.0 <- as.matrix(hbefElev[, c('Easting', 'Northing')])
X.0 <- cbind(1, elev.pred, elev.pred^2)
out.pred <- predict(out, X.0, coords.0, verbose = FALSE)

Learn more

The vignette("modelFitting") provides a more detailed description and tutorial of all functions in spOccupancy. For full statistical details on the MCMC samplers used in spOccupancy, see vignette("mcmcSamplers").