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spOccupancy <a href='https://doserlab.com/files/spoccupancy-web/'><img src="man/figures/logo.png" align="right" height="139" width="120"/></a>

spOccupancy fits single-species, multi-species, and integrated spatial occupancy models using Markov chain Monte Carlo (MCMC). Models are fit using Pólya-Gamma data augmentation. Spatial models are fit using either Gaussian processes or Nearest Neighbor Gaussian Processes (NNGP) for large spatial datasets. The package provides functionality for data integration of multiple single-species occupancy data sets using a joint likelihood framework. For multi-species models, spOccupancy provides functions to account for residual species correlations in a joint species distribution model framework while accounting for imperfect detection. spOccupancy also provides functions for multi-season (i.e., spatio-temporal) single-species occupancy models. Below we give a very brief introduction to some of the package’s functionality, and illustrate just one of the model fitting functions. For more information, see the resources referenced at the bottom of this page.

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() | Multi-species occupancy model | | spMsPGOcc() | Multi-species spatial occupancy model | | lfJSDM() | Joint species distribution model without imperfect detection | | sfJSDM() | Spatial joint species distribution model without imperfect detection | | lfMsPGOcc() | Multi-species occupancy model with species correlations | | sfMsPGOcc() | Multi-species spatial occupancy model with species correlations | | intMsPGOcc() | Multi-species occupancy model with multiple data sources | | tPGOcc() | Single-species multi-season occupancy model | | stPGOcc() | Single-species multi-season spatio-temporal occupancy model | | svcPGBinom() | Single-species spatially-varying coefficient GLM | | svcPGOcc() | Single-species spatially-varying coefficient occupancy model | | svcTPGBinom() | Single-species spatially-varying coefficient multi-season GLM | | svcTPGOcc() | Single-species spatially-varying coefficient multi-season occupancy model | | svcMsPGOcc() | Multi-species spatially-varying coefficient occupancy model | | tMsPGOcc() | Multi-species, multi-season occupancy model | | stMsPGOcc() | Multi-species, multi-season spatial occupancy model | | svcTMsPGOcc() | Multi-species, multi-season spatially-varying coefficient occupancy model | | tIntPGOcc() | Multi-season occupancy model with multiple data sources | | stIntPGOcc() | Spatial multi-season occupancy model with multiple data sources | | svcTIntPGOcc() | SVC multi-season occupancy model with multiple data sources | | postHocLM() | Fit a linear (mixed) model using estimates from a previous model fit | | ppcOcc() | Posterior predictive check using Bayesian p-values | | waicOcc() | Compute Widely Applicable Information Criterion (WAIC) | | updateMCMC() | Update an existing model object with more MCMC samples (in development) | | simOcc() | Simulate single-species occupancy data | | simTOcc() | Simulate single-species multi-season occupancy data | | simBinom() | Simulate detection-nondetection data with perfect detection | | simTBinom() | Simulate multi-season detection-nondetection data with perfect detection | | simMsOcc() | Simulate multi-species occupancy data | | simTMsOcc() | Simulate multi-species, multi-season occupancy data | | simIntOcc() | Simulate single-species occupancy data from multiple data sources | | simIntMsOcc() | Simulate multi-species occupancy data from multiple data sources | | simTIntOcc() | Simulate multi-season 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 detection (alpha) coefficients, the spatial variance (sigma.sq), the spatial decay 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 3 chains of the model for 20,000 iterations split into 800 batches each of length 25. For each chain, we discard the first 8000 iterations as burn-in and use a thinning rate of 4 for a resulting 9000 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 ?spPGOcc for more detailed information on all function arguments.

# Run the model
out <- spPGOcc(occ.formula = btbw.occ.formula,
               det.formula = btbw.det.formula,
               data = btbwHBEF, n.batch = 800, batch.length = 25,
               accept.rate = 0.43, cov.model = "exponential", 
               NNGP = TRUE, n.neighbors = 5, n.burn = 8000, 
               n.thin = 4, n.chains = 3, verbose = FALSE, 
               k.fold = 2, k.fold.threads = 2)

This will produce a large output object, and you can use str(out) to get an overview of what’s in there. Here we use the summary() function to print a concise but informative summary of the model fit.

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 = 800, batch.length = 25, accept.rate = 0.43, 
#>     verbose = FALSE, n.burn = 8000, n.thin = 4, n.chains = 3, 
#>     k.fold = 2, k.fold.threads = 2)
#> 
#> Samples per Chain: 20000
#> Burn-in: 8000
#> Thinning Rate: 4
#> Number of Chains: 3
#> Total Posterior Samples: 9000
#> Run Time (min): 1.3642
#> 
#> Occurrence (logit scale): 
#>                          Mean     SD    2.5%     50%   97.5%   Rhat  ESS
#> (Intercept)            3.9946 0.5810  3.0233  3.9337  5.2932 1.0302  354
#> scale(Elevation)      -0.5235 0.2193 -0.9785 -0.5145 -0.1082 1.0013 1368
#> I(scale(Elevation)^2) -1.1673 0.2117 -1.6341 -1.1489 -0.8003 1.0026  571
#> 
#> Detection (logit scale): 
#>                    Mean     SD    2.5%     50%  97.5%   Rhat  ESS
#> (Intercept)      0.6621 0.1136  0.4429  0.6602 0.8872 1.0009 8235
#> scale(day)       0.2912 0.0701  0.1526  0.2910 0.4294 1.0019 9000
#> scale(tod)      -0.0306 0.0699 -0.1672 -0.0299 0.1057 1.0025 9000
#> I(scale(day)^2) -0.0753 0.0861 -0.2456 -0.0753 0.0927 0.9999 9000
#> 
#> Spatial Covariance: 
#>            Mean     SD   2.5%    50%  97.5%   Rhat ESS
#> sigma.sq 1.1864 0.9200 0.2306 0.9314 3.5575 1.0336 160
#> phi      0.0075 0.0075 0.0007 0.0044 0.0272 1.0668 111

Posterior predictive check

The function ppcOcc performs a posterior predictive check on the resulting list from the call to spPGOcc.