This function fits a spatial occupancy model where the true occupancy is a function of a spatial process. An efficient Gibbs sampling algorithm is used by formulating the detection and occupancy process models with a probit model instead of the traditional logit based model.
spatial.occupancy(
detection.model,
occupancy.model,
spatial.model,
so.data,
prior,
control,
initial.values = NULL
)A formula object describing the detection portion of
the occupancy model. The variables described by the detection model are
located in the visit data frame of the so.data.
A formula object describing the fixed effects portion
of the spatial occupancy process. The variables described by the occupancy
model are located in the site data frame of an so.data object.
A named list object describing the spatial component of
the occupancy process. Currently the only possible models are ICAR, restricted spatial regression,
process convolution models, and no spatial model (i.e., eta = 0). Thus, spatial.model=list(model="icar",
threshold= ), spatial.model=list(model="rsr", threshold=, moran.cut=),
spatial.model=list(model="proc.conv", knots=), and spatial.model=list(model="none")
are the only forms that are accepted at present. The threshold
component is used the create neighborhoods in the ICAR and RSR models. All sites
within distance threshold of site i are considered neighbors of site
i. The moran.cut component is the cut-off for selecting
the spatial harmonics used in the restricted spatial regression model. The value must be between 1 and N and implies that
the eigen vectors associated with the largest moan.cut eigen values are used for the basis functions.
The item knots are xy locations of the discrete process
convolution knots.
An so.data object containing the observed occupancies,
detection covariates, site covariates, and site coordinates. This is created
via the make.so.data
A named list that provides the parameter values for the prior
distributions. At the current time the elements of the list must contain
a.tau and b.tau which are the parameters for the gamma prior on the spatial
process parameter in the occupancy model. Other elements may include
Q.b and mu.b which are the tolerance and mean for the beta
vector (detection parameters). Also Q.g and mu.g which are the
prior parameters for the occupancy model. If the Q.b and Q.g are left out,
the default is Q.b = 0 and Q.g = 0 (i.e., flat priors). If mu.b and mu.g are left out,
the default is zero vectors.
A named list with the control parameters for the MCMC. The
elements of the list must include: (1) burnin is the number of
iterations of burnin, (2) iter is the total number of iterations
retained for the MCMC sample, and (3) thin is the thining rate of the
chain. The real number of MCMC iterations is equal to iter*thin of
which iter - burnin are retained for posterior summary.
A named list that can include any or all of the following vectors or scalers
(1) beta, a vector of initial values for the detection parameters, (2) gamma, a vector or
initial values for the occupancy model, and (3) tau, an initial value for the spatial precision
parameter.
A list with the following elements:
An object of class
mcmc. The detection model parameters.
An object of
class mcmc. The occupancy model parameters.
An object of
class mcmc. The occupancy generating process
An
object of class mcmc. The realized occupancy at the time of the
survey
An object of
class mcmc. The variance parameter for the spatial model
A data frame with the spatial coordinates, site id, and posterior mean and variance of psi, eta, and real.occ
The posterior predictive loss criterion of Gelfand and Ghosh (1998; Biometrika 85:1-11) for model selection. The criterion is a combination of a goodness-of-fit measure, G.m, and a complexity measure, P.m, similar information criteria such as AIC and BIC. D.m = G.m + P.m. Lower values of D.m imply lower expected loss in predicting new data with the posterior model parameters.
The goodness-of-fit portion of D.m
The model complexity component of D.m
The detection model call.
The occupancy model call.
A character version of the joint occupancy and detection model call. This is useful for saving results.
A Gibbs sampler is run to draw an MCMC sample of the spatial occupancy
parameters beta (detection parameters), gamma (the occupancy
parameters), psi (the model occupancy generating process), and the
realized occupancy.