# Function for prediction at new locations for single-species integrated spatial occupancy models The function `predict` collects posterior predictive samples for a set of new locations given an object of class `spIntPGOcc`. ```r ## S3 method for class 'spIntPGOcc' predict(object, X.0, coords.0, n.omp.threads = 1, verbose = TRUE, n.report = 100, ignore.RE = FALSE, type = 'occupancy', ...) ``` ## Arguments - `object`: an object of class `spIntPGOcc`. - `X.0`: the design matrix for prediction locations. This should include a column of 1s for the intercept. Covariates should have the same column names as those used when fitting the model with `spIntPGOcc`. - `coords.0`: the spatial coordinates corresponding to `X.0`. Note that `spOccupancy` assumes coordinates are specified in a projected coordinate system. - `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. - `n.report`: the interval to report sampling progress. - `ignore.RE`: logical value that specifies whether or not to remove random occurrence (or detection if `type = 'detection'`) effects from the subsequent predictions. If `TRUE`, random effects will be included. If `FALSE`, random effects will be set to 0 and predictions will only be generated from the fixed effects. - `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. Note that prediction of detection probability is not currently supported for integrated models. - `...`: currently no additional arguments ## Author(s) Jeffrey W. Doser doserjef@msu.edu , Andrew O. Finley finleya@msu.edu ## Returns An object of class `predict.spIntPGOcc` that is a list comprised 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. The return object will include additional objects used for standard extractor functions. ## References Hooten, M. B., and Hefley, T. J. (2019). Bringing Bayesian models to life. CRC Press. ## Examples ```r set.seed(400) # 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 <- 8 J.y <- 8 J.all <- J.x * J.y # Number of data sources. n.data <- 4 # Sites for each data source. J.obs <- sample(ceiling(0.2 * J.all):ceiling(0.5 * J.all), n.data, replace = TRUE) # Replicates for each data source. n.rep <- list() for (i in 1:n.data) { n.rep[[i]] <- sample(1:4, size = J.obs[i], replace = TRUE) } # Occupancy covariates beta <- c(0.5, 0.5) p.occ <- length(beta) # Detection covariates alpha <- list() alpha[[1]] <- runif(2, 0, 1) alpha[[2]] <- runif(3, 0, 1) alpha[[3]] <- runif(2, -1, 1) alpha[[4]] <- runif(4, -1, 1) p.det.long <- sapply(alpha, length) p.det <- sum(p.det.long) sigma.sq <- 2 phi <- 3 / .5 sp <- TRUE # Simulate occupancy data. dat <- simIntOcc(n.data = n.data, J.x = J.x, J.y = J.y, J.obs = J.obs, n.rep = n.rep, beta = beta, alpha = alpha, sp = sp, phi = phi, sigma.sq = sigma.sq, cov.model = 'spherical') y <- dat$y X <- dat$X.obs X.p <- dat$X.p sites <- dat$sites X.0 <- dat$X.pred psi.0 <- dat$psi.pred coords <- as.matrix(dat$coords.obs) coords.0 <- as.matrix(dat$coords.pred) # Package all data into a list occ.covs <- X[, 2, drop = FALSE] colnames(occ.covs) <- c('occ.cov') det.covs <- list() # Add covariates one by one det.covs[[1]] <- list(det.cov.1.1 = X.p[[1]][, , 2]) det.covs[[2]] <- list(det.cov.2.1 = X.p[[2]][, , 2], det.cov.2.2 = X.p[[2]][, , 3]) det.covs[[3]] <- list(det.cov.3.1 = X.p[[3]][, , 2]) det.covs[[4]] <- list(det.cov.4.1 = X.p[[4]][, , 2], det.cov.4.2 = X.p[[4]][, , 3], det.cov.4.3 = X.p[[4]][, , 4]) data.list <- list(y = y, occ.covs = occ.covs, det.covs = det.covs, sites = sites, coords = coords) J <- length(dat$z.obs) # Initial values inits.list <- list(alpha = list(0, 0, 0, 0), beta = 0, phi = 3 / .5, sigma.sq = 2, w = rep(0, J), z = rep(1, J)) # Priors prior.list <- list(beta.normal = list(mean = 0, var = 2.72), alpha.normal = list(mean = list(0, 0, 0, 0), var = list(2.72, 2.72, 2.72, 2.72)), phi.unif = c(3/1, 3/.1), sigma.sq.ig = c(2, 2)) # Tuning tuning.list <- list(phi = 1) # Number of batches n.batch <- 40 # Batch length batch.length <- 25 # Note that this is just a test case and more iterations/chains may need to # be run to ensure convergence. out <- spIntPGOcc(occ.formula = ~ occ.cov, det.formula = list(f.1 = ~ det.cov.1.1, f.2 = ~ det.cov.2.1 + det.cov.2.2, f.3 = ~ det.cov.3.1, f.4 = ~ det.cov.4.1 + det.cov.4.2 + det.cov.4.3), data = data.list, inits = inits.list, n.batch = n.batch, batch.length = batch.length, accept.rate = 0.43, priors = prior.list, cov.model = "spherical", tuning = tuning.list, n.omp.threads = 1, verbose = TRUE, NNGP = TRUE, n.neighbors = 5, search.type = 'cb', n.report = 10, n.burn = 500, n.thin = 1) summary(out) # Predict at new locations ------------------------------------------------ out.pred <- predict(out, X.0, coords.0, verbose = FALSE) ```

predict.spIntPGOcc function