Function for prediction at new locations for single-species spatially-varying coefficient occupancy models

The function predict collects posterior predictive samples for a set of new locations given an object of class `svcPGOcc`. Prediction is possible for both the latent occupancy state as well as detection.

Usage

# S3 method for svcPGOcc
predict(object, X.0, coords.0, weights.0, n.omp.threads = 1, verbose = TRUE, 
        n.report = 100, ignore.RE = FALSE, type = 'occupancy', grid.index.0, ...)

Arguments

object: an object of class svcPGOcc
X.0: the design matrix of covariates at the prediction locations. This should include a column of 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 should be included as a column in the design matrix. The ordering of the levels should match the ordering used to fit the data in svcPGOcc. Columns should correspond to the order of how covariates were specified in the corresponding formula argument of svcPGOcc. Column names of the random effects must match the name of the random effects, if specified in the corresponding formula argument of svcPGOcc.
coords.0: the spatial coordinates corresponding to X.0. Note that spOccupancy assumes coordinates are specified in a projected coordinate system.
weights.0: not used for objects of class svcTPGOcc. Used when calling other functions.
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: a logical value indicating whether to include unstructured random effects for prediction. If TRUE, unstructured random effects will be ignored and prediction will only use the fixed effects and the spatial random effects. If FALSE, random effects will be included in the prediction for both observed and unobserved levels of the unstructured random effects.
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.
grid.index.0: an indexing vector used to specify how each row in X.0 corresponds to the coordinates specified in coords.0. Only relevant if the SVCs were estimated at a higher spatial resolution (e.g., grid cells) than point locations.
...: currently no additional arguments

Note

When ignore.RE = FALSE, both sampled levels and non-sampled levels of 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.

Author

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

References

Hooten, M. B., and Hefley, T. J. (2019). Bringing Bayesian models to life. CRC Press.

Value

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

psi.0.samples: a coda object of posterior predictive samples for the latent occurrence probability values.
z.0.samples: a coda object of posterior predictive samples for the latent occurrence values.
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().

When type = 'detection', the list consists of:

p.0.samples: a coda object of posterior predictive samples for the detection probability values.
run.time: execution time reported using proc.time().

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

Examples

set.seed(400)
# Simulate Data -----------------------------------------------------------
J.x <- 8
J.y <- 8
J <- J.x * J.y
n.rep <- sample(2:4, J, replace = TRUE)
beta <- c(0.5, 2)
p.occ <- length(beta)
alpha <- c(0, 1)
p.det <- length(alpha)
phi <- c(3 / .6, 3 / .8)
sigma.sq <- c(0.5, 0.9)
svc.cols <- c(1, 2)
dat <- simOcc(J.x = J.x, J.y = J.y, n.rep = n.rep, beta = beta, alpha = alpha, 
              sigma.sq = sigma.sq, phi = phi, sp = TRUE, cov.model = 'exponential', 
              svc.cols = svc.cols)
# Split into fitting and prediction data set
pred.indx <- sample(1:J, round(J * .5), replace = FALSE)
y <- dat$y[-pred.indx, ]
# Occupancy covariates
X <- dat$X[-pred.indx, ]
# Prediction covariates
X.0 <- dat$X[pred.indx, ]
# Detection covariates
X.p <- dat$X.p[-pred.indx, , ]
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, , drop = FALSE]

# Package all data into a list
occ.covs <- X[, -1, drop = FALSE]
colnames(occ.covs) <- c('occ.cov')
det.covs <- list(det.cov.1 = X.p[, , 2])
data.list <- list(y = y, 
                  occ.covs = occ.covs, 
                  det.covs = det.covs, 
                  coords = coords)

# Number of batches
n.batch <- 10
# Batch length
batch.length <- 25
n.iter <- n.batch * batch.length
# Priors 
prior.list <- list(beta.normal = list(mean = 0, var = 2.72), 
                   alpha.normal = list(mean = 0, var = 2.72),
                   sigma.sq.ig = list(a = 2, b = 0.5), 
                   phi.unif = list(a = 3/1, b = 3/.1)) 
# Initial values
inits.list <- list(alpha = 0, beta = 0,
                   phi = 3 / .5, 
                   sigma.sq = 0.5,
                   z = apply(y, 1, max, na.rm = TRUE))
# Tuning
tuning.list <- list(phi = 1) 

out <- svcPGOcc(occ.formula = ~ occ.cov, 
                det.formula = ~ det.cov.1, 
                data = data.list, 
                inits = inits.list, 
                n.batch = n.batch, 
                batch.length = batch.length, 
                accept.rate = 0.43, 
                priors = prior.list,
                cov.model = 'exponential', 
                tuning = tuning.list, 
                n.omp.threads = 1, 
                verbose = TRUE, 
                NNGP = TRUE, 
                svc.cols = c(1, 2),
                n.neighbors = 15, 
                search.type = 'cb', 
                n.report = 10, 
                n.burn = 50, 
                n.thin = 1)
#> ----------------------------------------
#> 	Preparing to run the model
#> ----------------------------------------
#> w is not specified in initial values.
#> Setting initial value to 0
#> ----------------------------------------
#> 	Building the neighbor list
#> ----------------------------------------
#> ----------------------------------------
#> Building the neighbors of neighbors list
#> ----------------------------------------
#> ----------------------------------------
#> 	Model description
#> ----------------------------------------
#> NNGP Occupancy model with Polya-Gamma latent
#> variable fit with 32 sites.
#> 
#> Samples per chain: 250 (10 batches of length 25)
#> Burn-in: 50 
#> Thinning Rate: 1 
#> Number of Chains: 1 
#> Total Posterior Samples: 200 
#> 
#> Number of spatially-varying coefficients: 2 
#> Using the exponential spatial correlation model.
#> 
#> Using 15 nearest neighbors.
#> 
#> Source compiled with OpenMP support and model fit using 1 thread(s).
#> 
#> Adaptive Metropolis with target acceptance rate: 43.0
#> ----------------------------------------
#> 	Chain 1
#> ----------------------------------------
#> Sampling ... 
#> Batch: 10 of 10, 100.00%

summary(out) 
#> 
#> Call:
#> svcPGOcc(occ.formula = ~occ.cov, det.formula = ~det.cov.1, data = data.list, 
#>     inits = inits.list, priors = prior.list, tuning = tuning.list, 
#>     svc.cols = c(1, 2), cov.model = "exponential", NNGP = TRUE, 
#>     n.neighbors = 15, search.type = "cb", n.batch = n.batch, 
#>     batch.length = batch.length, accept.rate = 0.43, n.omp.threads = 1, 
#>     verbose = TRUE, n.report = 10, n.burn = 50, n.thin = 1)
#> 
#> Samples per Chain: 250
#> Burn-in: 50
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 200
#> Run Time (min): 0.0041
#> 
#> Occurrence (logit scale): 
#>               Mean     SD    2.5%    50%  97.5% Rhat ESS
#> (Intercept) 0.6784 0.4649 -0.1881 0.6615 1.5878   NA 200
#> occ.cov     1.1567 0.5744  0.1486 1.1355 2.3007   NA  60
#> 
#> Detection (logit scale): 
#>               Mean     SD    2.5%    50%  97.5% Rhat ESS
#> (Intercept) 0.3672 0.3547 -0.3121 0.3888 1.1532   NA  85
#> det.cov.1   1.1323 0.3732  0.4377 1.1366 1.9229   NA  88
#> 
#> Spatial Covariance: 
#>                         Mean     SD   2.5%     50%   97.5% Rhat ESS
#> sigma.sq-(Intercept)  0.3932 0.4005 0.0900  0.2952  1.9538   NA  28
#> sigma.sq-occ.cov      0.4210 0.4452 0.0909  0.3113  1.3984   NA  26
#> phi-(Intercept)      20.6532 7.0367 7.3885 22.5316 29.1199   NA  17
#> phi-occ.cov          17.0577 6.1303 6.2573 17.2830 28.3586   NA  17

# Predict at new locations ------------------------------------------------
out.pred <- predict(out, X.0, coords.0, verbose = FALSE)