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

The function predict collects posterior predictive samples for a set of new locations given an object of class `tPGOcc`. 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 tPGOcc
predict(object, X.0, t.cols, ignore.RE = FALSE, type = 'occupancy', ...)

Arguments

object: an object of class tPGOcc
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 tPGOcc. The covariates should be organized in the same order as they were specified in the corresponding formula argument of tPGOcc. 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 tPGOcc. See example below.
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.
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, unstructured 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 and AR(1) random effects if the model was fit with ar1 = TRUE.
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 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 tPGOcc.

Author

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

Value

A list object of class predict.tPGOcc. 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.

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

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

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

Examples

set.seed(990)
# Sites
J.x <- 10
J.y <- 10
J <- J.x * J.y
# Primary time periods
n.time <- sample(10, J, replace = TRUE)
n.time.max <- max(n.time)
# Replicates
n.rep <- matrix(NA, J, max(n.time))
for (j in 1:J) {
  n.rep[j, 1:n.time[j]] <- sample(1:4, n.time[j], replace = TRUE)
}
# Occurrence --------------------------
beta <- c(0.4, 0.5, -0.9)
trend <- TRUE 
sp.only <- 0
psi.RE <- list()
# Detection ---------------------------
alpha <- c(-1, 0.7, -0.5)
p.RE <- list()

# Get all the data
dat <- simTOcc(J.x = J.x, J.y = J.y, n.time = n.time, n.rep = n.rep, 
               beta = beta, alpha = alpha, sp.only = sp.only, trend = trend, 
               psi.RE = psi.RE, p.RE = p.RE, sp = FALSE, ar1 = FALSE)

# Subset data for prediction
pred.indx <- sample(1:J, round(J * .25), replace = FALSE)
y <- dat$y[-pred.indx, , , drop = FALSE]
# Occupancy covariates
X <- dat$X[-pred.indx, , , drop = FALSE]
# Prediction covariates
X.0 <- dat$X[pred.indx, , , drop = FALSE]
# Detection covariates
X.p <- dat$X.p[-pred.indx, , , , drop = FALSE]
psi.0 <- dat$psi[pred.indx, ]

# Package all data into a list
# Occurrence
occ.covs <- list(int = X[, , 1], 
                 trend = X[, , 2], 
                 occ.cov.1 = X[, , 3]) 
# Detection
det.covs <- list(det.cov.1 = X.p[, , , 2], 
                 det.cov.2 = X.p[, , , 3]) 
# Data list bundle
data.list <- list(y = y, 
                  occ.covs = occ.covs,
                  det.covs = det.covs) 
# Priors
prior.list <- list(beta.normal = list(mean = 0, var = 2.72), 
                   alpha.normal = list(mean = 0, var = 2.72))

# Starting values
z.init <- apply(y, c(1, 2), function(a) as.numeric(sum(a, na.rm = TRUE) > 0))
inits.list <- list(beta = 0, alpha = 0, z = z.init)

n.batch <- 100
batch.length <- 25
n.burn <- 2000
n.thin <- 1

# Run the model
out <- tPGOcc(occ.formula = ~ trend + occ.cov.1, 
              det.formula = ~ det.cov.1 + det.cov.2, 
              data = data.list,
              inits = inits.list,
              priors = prior.list, 
              n.batch = n.batch,
              batch.length = batch.length,
              ar1 = FALSE,
              verbose = TRUE, 
              n.report = 500,
              n.burn = n.burn, 
              n.thin = n.thin,
              n.chains = 1) 
#> ----------------------------------------
#> 	Preparing the data
#> ----------------------------------------
#> ----------------------------------------
#> 	Model description
#> ----------------------------------------
#> Multi-season Occupancy Model with Polya-Gamma latent variable
#> fit with 75 sites and 10 primary time periods.
#> 
#> Samples per chain: 2500 (100 batches of length 25)
#> Burn-in: 2000 
#> Thinning Rate: 1 
#> Number of Chains: 1 
#> Total Posterior Samples: 500 
#> 
#> Source compiled with OpenMP support and model fit using 1 thread(s).
#> 
#> ----------------------------------------
#> 	Chain 1
#> ----------------------------------------
#> Sampling ... 
#> Batch: 100 of 100, 100.00%

# Predict at new sites across during time periods 1, 2, and 5
# Take a look at array of covariates for prediction
str(X.0)
#>  num [1:25, 1:10, 1:3] 1 1 1 1 1 1 1 1 1 1 ...
# Subset to only grab time periods 1, 2, and 5
t.cols <- c(1, 2, 5)
X.pred <- X.0[, t.cols, ]
out.pred <- predict(out, X.pred, t.cols = t.cols, type = 'occupancy')
str(out.pred)
#> List of 5
#>  $ psi.0.samples: num [1:500, 1:25, 1:3] 0.471 0.501 0.382 0.408 0.436 ...
#>  $ z.0.samples  : int [1:500, 1:25, 1:3] 0 0 0 0 1 0 1 0 1 0 ...
#>  $ run.time     : 'proc_time' Named num [1:5] 0.002 0.002 0.002 0 0
#>   ..- attr(*, "names")= chr [1:5] "user.self" "sys.self" "elapsed" "user.child" ...
#>  $ call         : language predict.tPGOcc(object = out, X.0 = X.pred, t.cols = t.cols, type = "occupancy")
#>  $ object.class : chr "tPGOcc"
#>  - attr(*, "class")= chr "predict.tPGOcc"