# Simulate Single-Species Detection-Nondetection Data

`simOcc.Rd`

The function `simOcc`

simulates single-species occurrence data for simulation studies, power assessments, or function testing. Data can be optionally simulated with a spatial Gaussian Process in the occurrence portion of the model. Non-spatial random intercepts can also be included in the detection or occurrence portions of the occupancy model.

## Arguments

- J.x
a single numeric value indicating the number of sites to simulate detection-nondetection data along the horizontal axis. Total number of sites with simulated data is \(J.x \times J.y\).

- J.y
a single numeric value indicating the number of sites to simulate detection-nondetection data along the vertical axis. Total number of sites with simulated data is \(J.x \times J.y\).

- n.rep
a numeric vector of length \(J = J.x \times J.y\) indicating the number of repeat visits at each of the \(J\) sites.

- beta
a numeric vector containing the intercept and regression coefficient parameters for the occupancy portion of the single-species occupancy model.

- alpha
a numeric vector containing the intercept and regression coefficient parameters for the detection portion of the single-species occupancy model.

- psi.RE
a list used to specify the non-spatial random intercepts included in the occupancy portion of the model. The list must have two tags:

`levels`

and`sigma.sq.psi`

.`levels`

is a vector of length equal to the number of distinct random intercepts to include in the model and contains the number of levels there are in each intercept.`sigma.sq.psi`

is a vector of length equal to the number of distinct random intercepts to include in the model and contains the variances for each random effect. If not specified, no random effects are included in the occupancy portion of the model.- p.RE
a list used to specify the non-spatial random intercepts included in the detection portion of the model. The list must have two tags:

`levels`

and`sigma.sq.p`

.`levels`

is a vector of length equal to the number of distinct random intercepts to include in the model and contains the number of levels there are in each intercept.`sigma.sq.p`

is a vector of length equal to the number of distinct random intercepts to include in the model and contains the variances for each random effect. If not specified, no random effects are included in the detection portion of the model.- 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 decay 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
a \(J \times p.occ\) numeric design matrix for the occupancy portion of the model.

- X.p
a three-dimensional numeric array with dimensions corresponding to sites, repeat visits, and number of detection regression coefficients. This is the design matrix used for the detection portion of the occupancy model.

- coords
a \(J \times 2\) numeric matrix of coordinates of each occupancy site. Required for spatial models.

- w
a \(J \times 1\) matrix of the spatial random effects. Only used to simulate data when

`sp = TRUE`

.- psi
a \(J \times 1\) matrix of the occupancy probabilities for each site.

- z
a length \(J\) vector of the latent occupancy states at each site.

- p
a

`J x max(n.rep)`

matrix of the detection probabilities for each site and replicate combination. Sites with fewer than`max(n.rep)`

replicates will contain`NA`

values.- y
a

`J x max(n.rep)`

matrix of the raw detection-nondetection data for each site and replicate combination.- X.p.re
a three-dimensional numeric array containing the levels of any detection random effect included in the model. Only relevant when detection random effects are specified in

`p.RE`

.- X.re
a numeric matrix containing the levels of any occurrence random effect included in the model. Only relevant when occurrence random effects are specified in

`psi.RE`

.- alpha.star
a numeric vector that contains the simulated detection random effects for each given level of the random effects included in the detection model. Only relevant when detection random effects are included in the model.

- beta.star
a numeric vector that contains the simulated occurrence random effects for each given level of the random effects included in the occurrence model. Only relevant when occurrence random effects are included in the model.

## Examples

```
set.seed(400)
J.x <- 10
J.y <- 10
n.rep <- rep(4, J.x * J.y)
beta <- c(0.5, -0.15)
alpha <- c(0.7, 0.4)
phi <- 3 / .6
sigma.sq <- 2
psi.RE <- list(levels = 10,
sigma.sq.psi = 1.2)
p.RE <- list(levels = 15,
sigma.sq.p = 0.8)
dat <- simOcc(J.x = J.x, J.y = J.y, n.rep = n.rep, beta = beta, alpha = alpha,
psi.RE = psi.RE, p.RE = p.RE, sp = TRUE, cov.model = 'spherical',
sigma.sq = sigma.sq, phi = phi)
```