Function for prediction at new locations for multi-season single-species spatially-varying coefficient binomial models

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

Usage

# S3 method for svcTPGBinom
predict(object, X.0, coords.0, t.cols, weights.0,  n.omp.threads = 1, 
        verbose = TRUE, n.report = 100, ignore.RE = FALSE, ...)

Arguments

object: an object of class svcTPGBinom
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 svcTPGBinom. The covariates should be organized in the same order as they were specified in the corresponding formula argument of svcTPGBinom. 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 svcTPGBinom. See example below.
coords.0: the spatial coordinates corresponding to X.0. Note that spOccupancy assumes coordinates are specified in a projected coordinate system.
weights.0: a numeric site by primary time period matrix containing the binomial weights (i.e., the total number of Bernoulli trials) at each site and primary time period. If weights.0 is not specified, we assume 1 trial at each site/primary time period (i.e., presence/absence).
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.
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.
...: 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 y.rep.samples portions of the output list from the model object of class svcTPGBinom.

Author

Jeffrey W. Doser doserjef@msu.edu,
Andrew O. Finley finleya@msu.edu

Value

A list object of class predict.svcTPGBinom that consists of:

psi.0.samples: a three-dimensional object of posterior predictive samples for the occurrence probability values with dimensions corresponding to posterior predictive sample, site, and primary time period.
y.0.samples: a three-dimensional object of posterior predictive samples for the predicted binomial data with dimensions corresponding to posterior predictive sample, site, and primary time period.
w.0.samples: a three-dimensional array of posterior predictive samples for the spatial random effects, with dimensions corresponding to MCMC iteration, coefficient, and site.
run.time: execution time reported using proc.time().

Examples

set.seed(1000)
# Sites
J.x <- 15
J.y <- 15
J <- J.x * J.y
# Years sampled
n.time <- sample(10, J, replace = TRUE)
# Binomial weights
weights <- matrix(NA, J, max(n.time))
for (j in 1:J) {
  weights[j, 1:n.time[j]] <- sample(5, n.time[j], replace = TRUE)
}
# Occurrence --------------------------
beta <- c(-2, -0.5, -0.2, 0.75)
p.occ <- length(beta)
trend <- TRUE
sp.only <- 0
psi.RE <- list()
# Spatial parameters ------------------
sp <- TRUE
svc.cols <- c(1, 2, 3)
p.svc <- length(svc.cols)
cov.model <- "exponential"
sigma.sq <- runif(p.svc, 0.1, 1)
phi <- runif(p.svc, 3/1, 3/0.2)
# Temporal parameters -----------------
ar1 <- TRUE
rho <- 0.8
sigma.sq.t <- 1

# Get all the data
dat <- simTBinom(J.x = J.x, J.y = J.y, n.time = n.time, weights = weights, beta = beta,
                 psi.RE = psi.RE, sp.only = sp.only, trend = trend, 
                 sp = sp, svc.cols = svc.cols,
                 cov.model = cov.model, sigma.sq = sigma.sq, phi = phi,
                 rho = rho, sigma.sq.t = sigma.sq.t, ar1 = TRUE, x.positive = FALSE)

# Prep the data for spOccupancy -------------------------------------------
# Subset data for prediction
pred.indx <- sample(1:J, round(J * .25), replace = FALSE)
y <- dat$y[-pred.indx, , drop = FALSE]
y.0 <- dat$y[pred.indx, , drop = FALSE]
# Occupancy covariates
X <- dat$X[-pred.indx, , , drop = FALSE]
# Prediction covariates
X.0 <- dat$X[pred.indx, , , drop = FALSE]
# Spatial coordinates
coords <- as.matrix(dat$coords[-pred.indx, ])
coords.0 <- as.matrix(dat$coords[pred.indx, ])
psi.0 <- dat$psi[pred.indx, ]
w.0 <- dat$w[pred.indx, ]
weights.0 <- weights[pred.indx, ]
weights <- weights[-pred.indx, ]

# Package all data into a list
covs <- list(int = X[, , 1],
             trend = X[, , 2],
             cov.1 = X[, , 3],
             cov.2 = X[, , 4])
# Data list bundle
data.list <- list(y = y,
                  covs = covs,
                  weights = weights,
                  coords = coords)
# Priors
prior.list <- list(beta.normal = list(mean = 0, var = 2.72),
                   sigma.sq.ig = list(a = 2, b = 1),
                   phi.unif = list(a = 3/1, b = 3/.1))

# Starting values
inits.list <- list(beta = beta, alpha = 0,
                   sigma.sq = 1, phi = 3 / 0.5, nu = 1)
# Tuning
tuning.list <- list(phi = 0.4, nu = 0.3, rho = 0.2)

# MCMC information
n.batch <- 2
n.burn <- 0
n.thin <- 1


out <- svcTPGBinom(formula = ~ trend + cov.1 + cov.2,
                   svc.cols = svc.cols,
                   data = data.list,
                   n.batch = n.batch,
                   batch.length = 25,
                   inits = inits.list,
                   priors = prior.list,
                   accept.rate = 0.43,
                   cov.model = "exponential",
                   ar1 = TRUE,
                   tuning = tuning.list,
                   n.omp.threads = 1,
                   verbose = TRUE,
                   NNGP = TRUE,
                   n.neighbors = 5,
                   n.report = 25,
                   n.burn = n.burn,
                   n.thin = n.thin,
                   n.chains = 1)
#> ----------------------------------------
#> 	Preparing the data
#> ----------------------------------------
#> No prior specified for rho.unif.
#> Setting uniform bounds to -1 and 1.
#> No prior specified for sigma.sq.t.
#> Using an inverse-Gamma prior with the shape parameter set to 2 and scale parameter to 0.5.
#> rho is not specified in initial values.
#> Setting initial value to random value from the prior distribution
#> sigma.sq.t is not specified in initial values.
#> Setting initial value to random value between 0.5 and 10
#> ----------------------------------------
#> 	Building the neighbor list
#> ----------------------------------------
#> ----------------------------------------
#> Building the neighbors of neighbors list
#> ----------------------------------------
#> ----------------------------------------
#> 	Model description
#> ----------------------------------------
#> Spatial NNGP Multi-season Binomial Model with Polya-Gamma latent
#> variable fit with 169 sites and 10 years.
#> 
#> Samples per chain: 50 (2 batches of length 25)
#> Burn-in: 0 
#> Thinning Rate: 1 
#> Number of Chains: 1 
#> Total Posterior Samples: 50 
#> 
#> Number of spatially-varying coefficients: 3 
#> Using the exponential spatial correlation model.
#> 
#> Using 5 nearest neighbors.
#> 
#> Using an AR(1) temporal autocorrelation matrix.
#> 
#> Source compiled with OpenMP support and model fit using 1 thread(s).
#> 
#> Adaptive Metropolis with target acceptance rate: 43.0
#> ----------------------------------------
#> 	Chain 1
#> ----------------------------------------
#> Sampling ... 
#> Batch: 2 of 2, 100.00%
# Predict at new locations ------------------------------------------------
out.pred <- predict(out, X.0, coords.0, t.cols = 1:max(n.time), 
                    weights = weights.0, n.report = 10)
#> ----------------------------------------
#> 	Prediction description
#> ----------------------------------------
#> Spatial NNGP Multi-season Occupancy model with Polya-Gamma latent
#> variable fit with 169 observations and 10 years.
#> 
#> Number of fixed covariates 4 (including intercept if specified).
#> 
#> Using the exponential spatial correlation model.
#> 
#> Using 5 nearest neighbors.
#> 
#> Number of MCMC samples 50.
#> 
#> Predicting at 56 non-sampled locations.
#> 
#> 
#> Source compiled with OpenMP support and model fit using 1 threads.
#> -------------------------------------------------
#> 		Predicting
#> -------------------------------------------------
#> Location: 10 of 56, 17.86%
#> Location: 20 of 56, 35.71%
#> Location: 30 of 56, 53.57%
#> Location: 40 of 56, 71.43%
#> Location: 50 of 56, 89.29%
#> Location: 56 of 56, 100.00%
#> Generating latent occupancy state
str(out.pred)
#> List of 6
#>  $ w.0.samples  : num [1:50, 1:3, 1:56] 0.5179 0.5078 0.569 -0.1911 -0.0777 ...
#>  $ psi.0.samples: num [1:50, 1:56, 1:10] 0.312 0.534 0.411 0.498 0.95 ...
#>  $ y.0.samples  : num [1:50, 1:56, 1:10] 0 2 3 0 4 4 3 3 1 2 ...
#>  $ run.time     : 'proc_time' Named num [1:5] 0.054 0.165 0.027 0 0
#>   ..- attr(*, "names")= chr [1:5] "user.self" "sys.self" "elapsed" "user.child" ...
#>  $ call         : language predict.svcTPGOcc(object = object, X.0 = X.0, coords.0 = coords.0, t.cols = t.cols,      weights.0 = weights.0, n| __truncated__ ...
#>  $ object.class : chr "svcTPGBinom"
#>  - attr(*, "class")= chr "predict.svcTPGOcc"