spOccupancy fits single-species, multi-species, and integrated spatial occupancy models using Markov Chain Monte Carlo (MCMC). Models are fit using Póly-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. As of v0.4.0, `spOccupancy`

provides functions for multi-season (i.e., spatio-temporal) single-species occupancy models. Below we provide a very brief introduction to some of the package’s functionality, and illustrate just one of the model fitting funcitons. 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 |

`tPGOcc()` |
Single-species multi-season occupancy model |

`stPGOcc()` |
Single-species multi-season spatio-temporal occupancy model |

`ppcOcc()` |
Posterior predictive check using Bayesian p-values |

`waicOcc()` |
Compute Widely Applicable Information Criterion (WAIC) |

`simOcc()` |
Simulate single-species occupancy data |

`simMsOcc()` |
Simulate multi-species 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 3 chains of the model each for 10,000 iterations split into 400 batches each of length 25. For each chain, we discard the first 6000 iterations as burn-in and use a thinning rate of 4 for a resulting 3000 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 = 400, batch.length = 25,
accept.rate = 0.43, cov.model = "exponential",
NNGP = TRUE, n.neighbors = 5, n.burn = 2000,
n.thin = 4, n.chains = 3, verbose = FALSE, k.fold = 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 = 400, batch.length = 25, accept.rate = 0.43,
#> verbose = FALSE, n.burn = 2000, n.thin = 4, n.chains = 3,
#> k.fold = 2)
#>
#> Samples per Chain: 10000
#> Burn-in: 2000
#> Thinning Rate: 4
#> Number of Chains: 3
#> Total Posterior Samples: 6000
#> Run Time (min): 1.4284
#>
#> Occurrence (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 3.9306 0.5843 2.9649 3.8718 5.3272 1.0703 278
#> scale(Elevation) -0.5134 0.2112 -0.9457 -0.5051 -0.1178 1.0070 1110
#> I(scale(Elevation)^2) -1.1388 0.2044 -1.6050 -1.1181 -0.7881 1.0705 466
#>
#> Detection (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.6663 0.1136 0.4486 0.6656 0.8900 0.9999 5769
#> scale(day) 0.2933 0.0704 0.1531 0.2929 0.4308 1.0000 6000
#> scale(tod) -0.0290 0.0702 -0.1638 -0.0293 0.1070 1.0024 6000
#> I(scale(day)^2) -0.0763 0.0863 -0.2447 -0.0768 0.0910 1.0011 6000
#>
#> Spatial Covariance:
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> sigma.sq 1.0481 0.9929 0.2094 0.7385 3.8056 1.2883 86
#> phi 0.0085 0.0078 0.0005 0.0053 0.0274 1.1606 53
```

### Posterior predictive check

The function `ppcOcc`

performs a posterior predictive check on the resulting list from the call to `spPGOcc`

. For binary data, we 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 then 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)
#>
#> Samples per Chain: 10000
#> Burn-in: 2000
#> Thinning Rate: 4
#> Number of Chains: 3
#> Total Posterior Samples: 6000
#>
#> Bayesian p-value: 0.4873
#> 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 (note that due to Monte Carlo error your results will differ slightly).

```
waicOcc(out)
#> elpd pD WAIC
#> -682.35028 20.86682 1406.43420
```

Alternatively, we can perform k-fold cross-validation (CV) 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 deviance scoring rule from the 2-fold cross-validation. If we have additional candidate models to compare this model with, then we might select for inference the one with the lowest value of this CV score.

```
out$k.fold.deviance
#> [1] 1496.56
```

### Prediction

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 the core functions in `spOccupancy`

. For full statistical details on the MCMC samplers for core functions in `spOccupancy`

, see `vignette("mcmcSamplers")`

. In addition, see our recent paper that describes the package in more detail (Doser et al. 2022a). For a detailed description and tutorial of joint species distribution models in `spOccupancy`

that account for residual species correlations, see `vignette("factorModels")`

, as well as `vignette("mcmcFactorModels")`

for full statistical details. For a description and tutoral of multi-season (spatio-temporal) occupancy models in `spOccupancy`

, see `vignette("spaceTimeModels")`

.

## References

Doser, J. W., Finley, A. O., Kéry, M., and Zipkin, E. F. (2022a). spOccupancy: An R package for single-species, multi-species, and integrated spatial occupancy models. Methods in Ecology and Evolution. https://doi.org/10.1111/2041-210X.13897.

Doser, J. W., Finley, A. O., and Banerjee, S. (2022b) Joint species distribution models with imperfect detection for high-dimensional spatial data. arXiv preprint arXiv:2204.02707.