# Function for prediction at new locations for multivariate spatially-varying coefficient GLMMs The function `predict` collects posterior predictive samples for a set of new locations given an object of class `svcMsAbund`. ```r ## S3 method for class 'svcMsAbund' predict(object, X.0, coords.0, n.omp.threads = 1, verbose = TRUE, n.report = 100, ignore.RE = FALSE, z.0.samples, ...) ``` ## Arguments - `object`: an object of class svcMsAbund - `X.0`: the design matrix of covariates at the prediction locations. This can be either a two-dimensional matrix with rows corresponding to sites and columns corresponding to covariates, or can be a three-dimensional array, with dimensions corresponding to site, replicate, 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 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 `svcMsAbund`. The covariates should be organized in the same order as they were specified in the corresponding formula argument of `svcMsAbund`. 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 `svcMsAbund`. See example below. - `coords.0`: the spatial coordinates corresponding to `X.0`. Note that `spAbundance` 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 unstructured random 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. - `z.0.samples`: a three-dimensional array with dimensions corresponding to MCMC samples, species, and prediction locations. The array contains the full posterior samples of the predicted binary portion of a zero-inflated Gaussian model. In the context of abundance models, this typically corresponds to estimates of the presence or absence of each species at the location. When using `spOccupancy` to generate the first stage samples of the zero-inflated Gaussian model, this is the object contained in the `z.0.samples` object of the predition function for the spOccupancy object. Ignored for all model types other than zero-inflated Gaussian. - `...`: 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 effect 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(s) Jeffrey W. Doser doserjef@msu.edu , Andrew O. Finley finleya@msu.edu ## Returns A list object of class `predict.svcMsAbund`. The list consists of: - **mu.0.samples**: a three or four-dimensional object of posterior predictive samples for the expected abundance values with dimensions corresponding to posterior predictive sample, species, site, and replicate. - **y.0.samples**: a three or four-dimensional object of posterior predictive samples for the abundance values with dimensions corresponding to posterior predictive sample, species, site, and replicate. - **w.0.samples**: a four-dimensional array of posterior predictive samples for the spatial factors for each spatially-varying coefficient. Dimensions correspond to MCMC sample, spatial factor, site, and spatially varying coefficient. The return object will include additional objects used for standard extractor functions. ## Examples ```r set.seed(408) J.x <- 8 J.y <- 8 J <- J.x * J.y n.rep <- rep(1, J) n.sp <- 6 # Community-level covariate effects beta.mean <- c(-2, 0.5) p.abund <- length(beta.mean) tau.sq.beta <- c(0.2, 1.2) mu.RE <- list() # Draw species-level effects from community means. beta <- matrix(NA, nrow = n.sp, ncol = p.abund) for (i in 1:p.abund) { beta[, i] <- rnorm(n.sp, beta.mean[i], sqrt(tau.sq.beta[i])) } sp <- TRUE factor.model <- TRUE n.factors <- 2 svc.cols <- c(1, 2) cov.model <- 'spherical' tau.sq <- runif(n.sp, 0.1, 2) phi <- runif(n.factors * length(svc.cols), 3 / 1, 3 / .1) dat <- simMsAbund(J.x = J.x, J.y = J.y, n.rep = n.rep, n.sp = n.sp, beta = beta, mu.RE = mu.RE, sp = sp, family = 'Gaussian', tau.sq = tau.sq, factor.model = factor.model, n.factors = n.factors, phi = phi, cov.model = cov.model, svc.cols = svc.cols) # Split into fitting and prediction data set 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] # Coordinates coords <- dat$coords[-pred.indx, ] # Prediction values y.0 <- dat$y[, pred.indx, drop = FALSE] X.0 <- dat$X[pred.indx, , drop = FALSE] coords.0 <- dat$coords[pred.indx, ] # Package all data into a list covs <- data.frame(abund.cov.1 = X[, 2]) data.list <- list(y = y, covs = covs, coords = coords) prior.list <- list(beta.comm.normal = list(mean = 0, var = 100), tau.sq.ig = list(a = .01, b = .01), phi.unif = list(a = 3 / 1, b = 3 / .1), tau.sq.beta.ig = list(a = .1, b = .1)) inits.list <- list(beta.comm = 0, beta = 0, kappa = 0.5, tau.sq = 1, phi = 3 / .5, tau.sq.beta = 1) tuning.list <- list(kappa = 0.3, beta = 0.1, lambda = 0.5, w = 0.5, phi = 1) # Small n.batch <- 2 batch.length <- 25 n.burn <- 20 n.thin <- 1 n.chains <- 1 out <- svcMsAbund(formula = ~ abund.cov.1, data = data.list, n.batch = n.batch, inits = inits.list, priors = prior.list, tuning = tuning.list, batch.length = batch.length, n.omp.threads = 1, svc.cols = c(1, 2), n.factors = n.factors, cov.model = 'exponential', family = 'Gaussian', verbose = TRUE, n.neighbors = 5, n.report = 1, n.burn = n.burn, n.thin = n.thin, n.chains = n.chains) # Predict at new locations out.pred <- predict(out, X.0, coords.0) str(out.pred) ```

predict.svcMsAbund function