# Simulate Single-Species Detection-Nondetection Data from Multiple Data Sources

`simIntOcc.Rd`

The function `simIntOcc`

simulates single-species detection-nondetection data from multiple data sources for simulation studies, power assessments, or function testing of integrated occupancy models. Data can optionally be simulated with a spatial Gaussian Process on the occurrence process.

## Usage

```
simIntOcc(n.data, J.x, J.y, J.obs, n.rep, n.rep.max, beta, alpha,
sp = FALSE, cov.model, sigma.sq, phi, nu, ...)
```

## Arguments

- n.data
an integer indicating the number of detection-nondetection data sources to simulate.

- J.x
a single numeric value indicating the number of sites across the region of interest along the horizontal axis. Total number of sites across the simulated region of interest is \(J.x \times J.y\).

- J.y
a single numeric value indicating the number of sites across the region of interest along the vertical axis. Total number of sites across the simulated region of interest is \(J.x \times J.y\).

- J.obs
a numeric vector of length

`n.data`

containing the number of sites to simulate each data source at. Data sources can be obtained at completely different sites, the same sites, or anywhere inbetween. Maximum number of sites a given data source is available at is equal to \(J = J.x \times J.y\).- n.rep
a list of length

`n.data`

. Each element is a numeric vector with length corresponding to the number of sites that given data source is observed at (in`J.obs`

). Each vector indicates the number of repeat visits at each of the sites for a given data source.- n.rep.max
a vector of numeric values indicating the maximum number of replicate surveys for each data set. This is an optional argument, with its default value set to

`max(n.rep)`

for each data set. This can be used to generate data sets with different types of missingness (e.g., simulate data across 20 days (replicate surveys) but sites are only sampled a maximum of ten times each).- beta
a numeric vector containing the intercept and regression coefficient parameters for the occurrence portion of the single-species occupancy model.

- alpha
a list of length

`n.data`

. Each element is a numeric vector containing the intercept and regression coefficient parameters for the detection portion of the single-species occupancy model for each data source.- sp
a logical value indicating whether to simulate a spatially-explicit occupancy model with a Gaussian process. By default set to

`FALSE`

.- cov.model
a quoted keyword that specifies the covariance function used to model the spatial dependence structure among the latent occurrence values. Supported covariance model key words are:

`"exponential"`

,`"matern"`

,`"spherical"`

, and`"gaussian"`

.- sigma.sq
a numeric value indicating the spatial variance parameter. Ignored when

`sp = FALSE`

.- phi
a numeric value indicating the spatial range parameter. Ignored when

`sp = FALSE`

.- nu
a numeric value indicating the spatial smoothness parameter. Only used when

`sp = TRUE`

and`cov.model = "matern"`

.- ...
currently no additional arguments

## Author

Jeffrey W. Doser doserjef@msu.edu,

Andrew O. Finley finleya@msu.edu

## Value

A list comprised of:

- X.obs
a numeric design matrix for the occurrence portion of the model. This matrix contains the intercept and regression coefficients for only the observed sites.

- X.pred
a numeric design matrix for the occurrence portion of the model at sites where there are no observed data sources.

- X.p
a list of design matrices for the detection portions of the integrated occupancy model. Each element in the list is a design matrix of detection covariates for each data source.

- coords.obs
a numeric matrix of coordinates of each observed site. Required for spatial models.

- coords.pred
a numeric matrix of coordinates of each site in the study region without any data sources. Only used for spatial models.

- D.obs
a distance matrix of observed sites. Only used for spatial models.

- D.pred
a distance matrix of sites in the study region without any observed data. Only used for spatial models.

- w.obs
a matrix of the spatial random effects at observed locations. Only used to simulate data when

`sp = TRUE`

.

- w.pred
a matrix of the spatial random random effects at locations without any observation.

- psi.obs
a matrix of the occurrence probabilities for each observed site.

- psi.pred
a matrix of the occurrence probabilities for sites without any observations.

- z.obs
a vector of the latent occurrence states at each observed site.

- z.pred
a vector of the latent occurrence states at each site without any observations.

- p
a list of detection probability matrices for each of the

`n.data`

data sources.- y
a list of matrices of the raw detection-nondetection data for each site and replicate combination.

## Examples

```
set.seed(400)
# Simulate Data -----------------------------------------------------------
J.x <- 15
J.y <- 15
J.all <- J.x * J.y
# Number of data sources.
n.data <- 4
# Sites for each data source.
J.obs <- sample(ceiling(0.2 * J.all):ceiling(0.5 * J.all), n.data, replace = TRUE)
# Replicates for each data source.
n.rep <- list()
for (i in 1:n.data) {
n.rep[[i]] <- sample(1:4, size = J.obs[i], replace = TRUE)
}
# Occupancy covariates
beta <- c(0.5, 1, -3)
p.occ <- length(beta)
# Detection covariates
alpha <- list()
for (i in 1:n.data) {
alpha[[i]] <- runif(sample(1:4, 1), -1, 1)
}
p.det.long <- sapply(alpha, length)
p.det <- sum(p.det.long)
sigma.sq <- 2
phi <- 3 / .5
sp <- TRUE
# Simulate occupancy data.
dat <- simIntOcc(n.data = n.data, J.x = J.x, J.y = J.y, J.obs = J.obs,
n.rep = n.rep, beta = beta, alpha = alpha, sp = TRUE,
cov.model = 'gaussian', sigma.sq = sigma.sq, phi = phi)
```