Function for prediction at new locations for spatial factor multi-species occupancy models
predict.sfMsPGOcc.RdThe function predict collects posterior predictive samples for a set of new locations given an object of class `sfMsPGOcc`. Prediction is possible for both the latent occupancy state as well as detection.
Usage
# S3 method for sfMsPGOcc
predict(object, X.0, coords.0, n.omp.threads = 1, verbose = TRUE,
n.report = 100, ignore.RE = FALSE, type = 'occupancy', grid.index.0, ...)Arguments
- object
an object of class sfMsPGOcc
- 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 insfMsPGOcc. Columns should correspond to the order of how covariates were specified in the corresponding formula argument ofsfMsPGOcc. Column names of the random effects must match the name of the random effects, if specified in the corresponding formula argument ofsfMsPGOcc.- coords.0
the spatial coordinates corresponding to
X.0. Note thatspOccupancyassumes 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.threadsup 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
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.
- 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.0corresponds to the coordinates specified incoords.0. Only relevant if the spatial random effect was 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
Value
An list object of class predict.sfMsPGOcc. When type = 'occupancy', the list consists of:
- psi.0.samples
a three-dimensional array of posterior predictive samples for the latent occurrence probability values.
- z.0.samples
a three-dimensional array of posterior predictive samples for the latent occurrence values.
- w.0.samples
a three-dimensional array of posterior predictive samples for the latent spatial factors.
- run.time
execution time reported using
proc.time().
When type = 'detection', the list consists of:
- p.0.samples
a three-dimensional array 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 <- 7
J.y <- 7
J <- J.x * J.y
n.rep <- sample(2:4, size = J, replace = TRUE)
N <- 5
# Community-level covariate effects
# Occurrence
beta.mean <- c(0.2, -0.15)
p.occ <- length(beta.mean)
tau.sq.beta <- c(0.6, 0.3)
# Detection
alpha.mean <- c(0.5, 0.2, -.2)
tau.sq.alpha <- c(0.2, 0.3, 0.8)
p.det <- length(alpha.mean)
# Draw species-level effects from community means.
beta <- matrix(NA, nrow = N, ncol = p.occ)
alpha <- matrix(NA, nrow = N, ncol = p.det)
for (i in 1:p.occ) {
beta[, i] <- rnorm(N, beta.mean[i], sqrt(tau.sq.beta[i]))
}
for (i in 1:p.det) {
alpha[, i] <- rnorm(N, alpha.mean[i], sqrt(tau.sq.alpha[i]))
}
n.factors <- 3
phi <- runif(n.factors, 3/1, 3/.4)
sp <- TRUE
dat <- simMsOcc(J.x = J.x, J.y = J.y, n.rep = n.rep, N = N, beta = beta, alpha = alpha,
phi = phi, sigma.sq = sigma.sq, sp = TRUE, cov.model = 'exponential',
factor.model = TRUE, n.factors = n.factors)
#> sigma.sq is specified but will be set to 1 for spatial latent factor model
# Number of batches
n.batch <- 10
# Batch length
batch.length <- 25
n.samples <- n.batch * batch.length
# Split into fitting and prediction data set
pred.indx <- sample(1:J, round(J * .25), replace = FALSE)
y <- dat$y[, -pred.indx, ]
# Occupancy covariates
X <- dat$X[-pred.indx, ]
# Coordinates
coords <- as.matrix(dat$coords[-pred.indx, ])
# Detection covariates
X.p <- dat$X.p[-pred.indx, , ]
# Prediction values
X.0 <- dat$X[pred.indx, ]
coords.0 <- as.matrix(dat$coords[pred.indx, ])
psi.0 <- dat$psi[, pred.indx]
# Package all data into a list
occ.covs <- X[, 2, drop = FALSE]
colnames(occ.covs) <- c('occ.cov')
det.covs <- list(det.cov.1 = X.p[, , 2],
det.cov.2 = X.p[, , 3])
data.list <- list(y = y,
occ.covs = occ.covs,
det.covs = det.covs,
coords = coords)
# Priors
prior.list <- list(beta.comm.normal = list(mean = 0, var = 2.72),
alpha.comm.normal = list(mean = 0, var = 2.72),
tau.sq.beta.ig = list(a = 0.1, b = 0.1),
tau.sq.alpha.ig = list(a = 0.1, b = 0.1),
phi.unif = list(a = 3/1, b = 3/.1),
sigma.sq.ig = list(a = 2, b = 2))
# Starting values
lambda.inits <- matrix(0, N, n.factors)
diag(lambda.inits) <- 1
lambda.inits[lower.tri(lambda.inits)] <- rnorm(sum(lower.tri(lambda.inits)))
inits.list <- list(alpha.comm = 0,
beta.comm = 0,
beta = 0,
alpha = 0,
tau.sq.beta = 1,
tau.sq.alpha = 1,
phi = 3 / .5,
sigma.sq = 2,
lambda = lambda.inits,
z = apply(y, c(1, 2), max, na.rm = TRUE))
# Tuning
tuning.list <- list(phi = 1)
out <- sfMsPGOcc(occ.formula = ~ occ.cov,
det.formula = ~ det.cov.1 + det.cov.2,
data = data.list,
inits = inits.list,
n.batch = n.batch,
batch.length = batch.length,
accept.rate = 0.43,
n.factors = 3,
priors = prior.list,
cov.model = "exponential",
tuning = tuning.list,
n.omp.threads = 1,
verbose = TRUE,
NNGP = TRUE,
n.neighbors = 5,
search.type = 'cb',
n.report = 10,
n.burn = 100,
n.thin = 1)
#> ----------------------------------------
#> Preparing to run the model
#> ----------------------------------------
#> ----------------------------------------
#> Building the neighbor list
#> ----------------------------------------
#> ----------------------------------------
#> Building the neighbors of neighbors list
#> ----------------------------------------
#> ----------------------------------------
#> Model description
#> ----------------------------------------
#> Spatial Factor NNGP Multi-species Occupancy Model with Polya-Gamma latent
#> variable fit with 37 sites and 5 species.
#>
#> Samples per chain: 250 (10 batches of length 25)
#> Burn-in: 100
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 150
#>
#> Using the exponential spatial correlation model.
#>
#> Using 3 latent spatial factors.
#> Using 5 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, level = 'both')
#>
#> Call:
#> sfMsPGOcc(occ.formula = ~occ.cov, det.formula = ~det.cov.1 +
#> det.cov.2, data = data.list, inits = inits.list, priors = prior.list,
#> tuning = tuning.list, cov.model = "exponential", NNGP = TRUE,
#> n.neighbors = 5, search.type = "cb", n.factors = 3, n.batch = n.batch,
#> batch.length = batch.length, accept.rate = 0.43, n.omp.threads = 1,
#> verbose = TRUE, n.report = 10, n.burn = 100, n.thin = 1)
#>
#> Samples per Chain: 250
#> Burn-in: 100
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 150
#> Run Time (min): 0.0039
#>
#> ----------------------------------------
#> Community Level
#> ----------------------------------------
#> Occurrence Means (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.1279 0.4809 -0.5962 0.1139 1.0244 NA 107
#> occ.cov 0.1500 0.3667 -0.5559 0.1252 0.8037 NA 33
#>
#> Occurrence Variances (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.8961 1.901 0.0475 0.3950 4.9997 NA 85
#> occ.cov 0.3125 0.353 0.0454 0.1914 1.4483 NA 32
#>
#> Detection Means (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.8142 0.3624 0.0958 0.8084 1.6055 NA 29
#> det.cov.1 -0.1869 0.3415 -0.8131 -0.2243 0.6684 NA 88
#> det.cov.2 -0.4910 0.4105 -1.2354 -0.5374 0.3462 NA 74
#>
#> Detection Variances (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.4905 0.5251 0.0568 0.3149 2.1140 NA 82
#> det.cov.1 0.7193 1.0831 0.0887 0.4034 3.4251 NA 83
#> det.cov.2 0.6256 1.0837 0.0444 0.2575 3.0426 NA 67
#>
#> ----------------------------------------
#> Species Level
#> ----------------------------------------
#> Occurrence (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept)-sp1 0.6715 0.3761 -0.1709 0.6961 1.3156 NA 55
#> (Intercept)-sp2 0.5882 0.5051 -0.2428 0.5514 1.7071 NA 55
#> (Intercept)-sp3 0.1843 0.5041 -0.8952 0.1968 1.1181 NA 48
#> (Intercept)-sp4 -0.2304 0.4729 -1.2982 -0.2257 0.6187 NA 31
#> (Intercept)-sp5 -0.3415 0.4893 -1.4413 -0.2936 0.4630 NA 37
#> occ.cov-sp1 -0.0575 0.3364 -0.7133 -0.0834 0.6045 NA 39
#> occ.cov-sp2 0.1964 0.3867 -0.5235 0.2169 0.9118 NA 58
#> occ.cov-sp3 0.1423 0.3432 -0.4604 0.1385 0.7831 NA 59
#> occ.cov-sp4 0.4982 0.4274 -0.1825 0.4545 1.5038 NA 26
#> occ.cov-sp5 0.0507 0.4105 -0.8291 0.0599 0.7582 NA 45
#>
#> Detection (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept)-sp1 1.0610 0.2554 0.5744 1.0227 1.5660 NA 146
#> (Intercept)-sp2 0.9551 0.2835 0.3985 0.9510 1.4898 NA 91
#> (Intercept)-sp3 0.0828 0.3857 -0.7113 0.0492 0.7735 NA 30
#> (Intercept)-sp4 0.8353 0.3202 0.1672 0.8423 1.4155 NA 33
#> (Intercept)-sp5 1.1804 0.3386 0.5211 1.1917 1.7924 NA 63
#> det.cov.1-sp1 -0.0049 0.2958 -0.5699 -0.0183 0.5093 NA 72
#> det.cov.1-sp2 -0.7877 0.2645 -1.2454 -0.7849 -0.3337 NA 45
#> det.cov.1-sp3 0.4804 0.2846 -0.0461 0.4732 1.0194 NA 86
#> det.cov.1-sp4 -0.5717 0.3807 -1.5004 -0.5610 0.0679 NA 44
#> det.cov.1-sp5 -0.3540 0.3291 -0.9798 -0.3291 0.1931 NA 53
#> det.cov.2-sp1 -0.4193 0.2798 -0.9672 -0.3734 0.0796 NA 80
#> det.cov.2-sp2 -0.3318 0.2617 -0.8557 -0.3387 0.1666 NA 75
#> det.cov.2-sp3 -1.1993 0.4123 -2.2382 -1.1685 -0.4733 NA 50
#> det.cov.2-sp4 -0.5172 0.3994 -1.3174 -0.4779 0.2290 NA 61
#> det.cov.2-sp5 -0.3699 0.4016 -1.1606 -0.4059 0.4463 NA 54
#>
#> ----------------------------------------
#> Spatial Covariance
#> ----------------------------------------
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> phi-1 14.4708 7.4146 3.5139 13.0261 29.2457 NA 15
#> phi-2 19.7087 8.2989 6.8214 19.3789 29.9599 NA 5
#> phi-3 15.4539 7.0912 4.5355 16.4643 27.6845 NA 15
# Predict at new locations ------------------------------------------------
out.pred <- predict(out, X.0, coords.0, verbose = FALSE)