predict.stIntPGOcc function

Function for prediction at new locations for multi-season single-species spatial integrated occupancy models

The function predict collects posterior predictive samples for a set of new locations given an object of class stIntPGOcc. Prediction is only currently possible for the latent occupancy state. Predictions are currently only possible for sampled primary time periods.

## S3 method for class 'stIntPGOcc'
predict(object, X.0, coords.0, t.cols, n.omp.threads = 1, 
                          verbose = TRUE, n.report = 100, 
                          ignore.RE = FALSE, type = 'occupancy', 
                          forecast = FALSE, ...)

Arguments

• object: an object of class stIntPGOcc
• X.0: the design matrix of covariates at the prediction locations. This should be a three-dimensional array, with dimensions corresponding to site, primary time period, and covariate, respectively. Note that the first covariate should consist of all 1s for the intercept if an intercept is included in the model. If random effects are included in the occupancy (or detection if type = 'detection') portion of the model, the levels of the random effects at the new locations/time periods should be included as an element of the three-dimensional array. The ordering of the levels should match the ordering used to fit the data in stIntPGOcc. The covariates should be organized in the same order as they were specified in the corresponding formula argument of stIntPGOcc. Names of the third dimension (covariates) of any random effects in X.0 must match the name of the random effects used to fit the model, if specified in the corresponding formula argument of stIntPGOcc. See example below.
• coords.0: the spatial coordinates corresponding to X.0. Note that spOccupancy assumes coordinates are specified in a projected coordinate system.
• t.cols: an indexing vector used to denote which primary time periods are contained in the design matrix of covariates at the prediction locations (X.0). The values should denote the specific primary time periods used to fit the model. The values should indicate the columns in data$y used to fit the model for which prediction is desired. See example below. Not required when forecast = TRUE.
• n.omp.threads: a positive integer indicating the number of threads to use for SMP parallel processing. The package must be compiled for OpenMP support. For most Intel-based machines, we recommend setting n.omp.threads up to the number of hyperthreaded cores. Note, n.omp.threads > 1 might not work on some systems.
• verbose: if TRUE, model specification and progress of the sampler is printed to the screen. Otherwise, nothing is printed to the screen.
• ignore.RE: logical value that specifies whether or not to remove random unstructured occurrence (or detection if type = 'detection') effects from the subsequent predictions. If TRUE, random effects will be included. If FALSE, unstructured random effects will be set to 0 and predictions will only be generated from the fixed effects, the spatial random effects, and AR(1) random effects if the model was fit with ar1 = TRUE.
• n.report: the interval to report sampling progress.
• type: a quoted keyword indicating what type of prediction to produce. Valid keywords are 'occupancy' to predict latent occupancy probability and latent occupancy values (this is the default), or 'detection' to predict detection probability given new values of detection covariates. Currently only occupancy prediction is supported for integrated models.
• forecast: a logical value indicating whether prediction is occurring at non-sampled primary time periods (e.g., forecasting).
• ...: currently no additional arguments

Note

When ignore.RE = FALSE, both sampled levels and non-sampled levels of unstructured random effects are supported for prediction. For sampled levels, the posterior distribution for the random intercept corresponding to that level of the random effect will be used in the prediction. For non-sampled levels, random values are drawn from a normal distribution using the posterior samples of the random effect variance, which results in fully propagated uncertainty in predictions with models that incorporate random effects.

Occurrence predictions at sites that are only sampled for a subset of the total number of primary time periods are obtained directly when fitting the model. See the psi.samples and z.samples portions of the output list from the model object of class stIntPGOcc.

Author(s)

Jeffrey W. Doser doserjef@msu.edu ,

Andrew O. Finley finleya@msu.edu

Returns

A list object of class predict.stIntPGOcc. When type = 'occupancy', the list consists of:

• psi.0.samples: a three-dimensional object of posterior predictive samples for the latent occupancy probability values with dimensions corresponding to posterior predictive sample, site, and primary time period.

• z.0.samples: a three-dimensional object of posterior predictive samples for the latent occupancy values with dimensions corresponding to posterior predictive sample, site, and primary time period.

• w.0.samples: a coda object of posterior predictive samples for the latent spatial random effects.

The return object will include additional objects used for standard extractor functions.

Examples

set.seed(332)

# Simulate Data -----------------------------------------------------------
# Number of locations in each direction. This is the total region of interest
# where some sites may or may not have a data source.
J.x <- 15 
J.y <- 15
J.all <- J.x * J.y
# Number of data sources.
n.data <- 3
# Sites for each data source.
J.obs <- sample(ceiling(0.2 * J.all):ceiling(0.4 * J.all), n.data, replace = TRUE)
# Maximum number of years for each data set
n.time.max <- c(4, 8, 10)
# Number of years each site in each data set is sampled
n.time <- list()
for (i in 1:n.data) {
  n.time[[i]] <- sample(1:n.time.max[i], J.obs[i], replace = TRUE)
}
# Replicates for each data source.
n.rep <- list()
for (i in 1:n.data) {
  n.rep[[i]] <- matrix(NA, J.obs[i], n.time.max[i])
  for (j in 1:J.obs[i]) {
    n.rep[[i]][j, sample(1:n.time.max[i], n.time[[i]][j], replace = FALSE)] <- 
      sample(1:4, n.time[[i]][j], replace = TRUE)
  }
}
# Total number of years across all data sets
n.time.total <- 10
# List denoting the specific years each data set was sampled during. 
data.seasons <- list()
for (i in 1:n.data) {
  data.seasons[[i]] <- sort(sample(1:n.time.total, n.time.max[i], replace = FALSE))
}

# Occupancy covariates
beta <- c(0, 0.4, 0.3)
trend <- TRUE
# Random occupancy covariates
psi.RE <- list()
p.occ <- length(beta)
# Detection covariates
alpha <- list()
alpha[[1]] <- c(0, 0.2, -0.5)
alpha[[2]] <- c(-1, 0.5, 0.3, -0.8)
alpha[[3]] <- c(-0.5, 1)

p.RE <- list()
p.det.long <- sapply(alpha, length)
p.det <- sum(p.det.long)

# Spatial parameters
sigma.sq <- 0.9
phi <- 3 / .5

# Simulate occupancy data.
dat <- simTIntOcc(n.data = n.data, J.x = J.x, J.y = J.y, J.obs = J.obs,
                  n.time = n.time, data.seasons = data.seasons, n.rep = n.rep,
                  beta = beta, alpha = alpha, trend = trend, 
                  psi.RE = psi.RE, p.RE = p.RE, sp = TRUE, 
                  sigma.sq = sigma.sq, phi = phi, cov.model = 'exponential')

y <- dat$y
X <- dat$X.obs
X.p <- dat$X.p
sites <- dat$sites
coords <- dat$coords.obs

# Package all data into a list
occ.covs <- list(trend = X[, , 2], 
                 occ.cov.1 = X[, , 3])
det.covs <- list()
# Add covariates one by one
det.covs[[1]] <- list(det.cov.1.1 = X.p[[1]][, , , 2],
                      det.cov.1.2 = X.p[[1]][, , , 3])
det.covs[[2]] <- list(det.cov.2.1 = X.p[[2]][, , , 2],
                      det.cov.2.2 = X.p[[2]][, , , 3],
                      det.cov.2.3 = X.p[[2]][, , , 4])
det.covs[[3]] <- list(det.cov.3.1 = X.p[[3]][, , , 2])
data.list <- list(y = y, occ.covs = occ.covs, det.covs = det.covs,
                  sites = sites, seasons = data.seasons, coords = coords)

# Testing
occ.formula <- ~ trend + occ.cov.1
# Note that the names are not necessary.
det.formula <- list(f.1 = ~ det.cov.1.1 + det.cov.1.2,
                    f.2 = ~ det.cov.2.1 + det.cov.2.2 + det.cov.2.3,
                    f.3 = ~ det.cov.3.1)

# NOTE: this is a short run of the model, in reality we would run the 
#       model for much longer.
out <- stIntPGOcc(occ.formula = occ.formula,
                 det.formula = det.formula,
                 data = data.list,
                 NNGP = TRUE, 
                 n.neighbors = 15, 
                 cov.model = 'exponential',
                 n.batch = 3,
                 batch.length = 25, 
                 n.report = 1,
                 n.burn = 25,
                 n.thin = 1,
                 n.chains = 1)

t.cols <- 1:n.time.total
out.pred <- predict(out, X.0 = dat$X.pred, coords.0 = dat$coords.pred, 
                    t.cols = t.cols, type = 'occupancy')
str(out.pred)