Function for prediction at new locations for spatially varying coefficient multi-species occupancy models
predict.svcMsPGOcc.RdThe function predict collects posterior predictive samples for a set of new locations given an object of class `svcMsPGOcc`. Prediction is possible for both the latent occupancy state as well as detection.
Usage
# S3 method for svcMsPGOcc
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 svcMsPGOcc
- 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 insvcMsPGOcc. Columns should correspond to the order of how covariates were specified in the corresponding formula argument ofsvcMsPGOcc. Column names of the random effects must match the name of the random effects, if specified in the corresponding formula argument ofsvcMsPGOcc.- 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.
- ...
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.svcMsPGOcc. 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 four-dimensional array of posterior predictive samples for the spatially-varying coefficients, with dimensions corresponding to MCMC sample, spatial factor, site, and spatially varying coefficient.
- 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 <- 10
J.y <- 10
J <- J.x * J.y
n.rep <- sample(5, size = J, replace = TRUE)
N <- 6
# Community-level covariate effects
# Occurrence
beta.mean <- c(0.2, -0.2, 0.3, -0.1, 0.4)
p.occ <- length(beta.mean)
tau.sq.beta <- c(0.6, 1.5, 0.4, 0.5, 0.3)
# Detection
alpha.mean <- c(0, 1.2, -0.5)
tau.sq.alpha <- c(1, 0.5, 1.3)
p.det <- length(alpha.mean)
# No random effects
psi.RE <- list()
p.RE <- list()
# 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]))
}
# Number of spatial factors for each SVC
n.factors <- 2
# The intercept and first two covariates have spatially-varying effects
svc.cols <- c(1, 2, 3)
p.svc <- length(svc.cols)
q.p.svc <- n.factors * p.svc
# Spatial decay parameters
phi <- runif(q.p.svc, 3 / 0.9, 3 / 0.1)
# A length N vector indicating the proportion of simulated locations
# that are within the range for a given species.
range.probs <- runif(N, 1, 1)
factor.model <- TRUE
cov.model <- 'spherical'
sp <- TRUE
dat <- simMsOcc(J.x = J.x, J.y = J.y, n.rep = n.rep, N = N, beta = beta, alpha = alpha,
psi.RE = psi.RE, p.RE = p.RE, phi = phi, sp = sp, svc.cols = svc.cols,
cov.model = cov.model, n.factors = n.factors,
factor.model = factor.model, range.probs = range.probs)
# 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, ])
# Prep data for spOccupancy -----------------------------------------------
# Occurrence covariates
occ.covs <- cbind(X)
colnames(occ.covs) <- c('int', 'occ.cov.1', 'occ.cov.2', 'occ.cov.3',
'occ.cov.4')
# Detection covariates
det.covs <- list(det.cov.1 = X.p[, , 2],
det.cov.2 = X.p[, , 3])
# Data list
data.list <- list(y = y, coords = coords, occ.covs = occ.covs,
det.covs = det.covs)
# 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))
inits.list <- list(alpha.comm = 0,
beta.comm = 0,
beta = 0,
alpha = 0,
tau.sq.beta = 1,
tau.sq.alpha = 1,
z = apply(y, c(1, 2), max, na.rm = TRUE))
# Tuning
tuning.list <- list(phi = 1)
# Number of batches
n.batch <- 2
# Batch length
batch.length <- 25
n.burn <- 0
n.thin <- 1
n.samples <- n.batch * batch.length
out <- svcMsPGOcc(occ.formula = ~ occ.cov.1 + occ.cov.2 + occ.cov.3 +
occ.cov.4,
det.formula = ~ det.cov.1 + det.cov.2,
data = data.list,
inits = inits.list,
n.batch = n.batch,
n.factors = n.factors,
batch.length = batch.length,
std.by.sp = TRUE,
accept.rate = 0.43,
priors = prior.list,
svc.cols = svc.cols,
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 = n.burn,
n.thin = n.thin,
n.chains = 1)
#> ----------------------------------------
#> Preparing to run the model
#> ----------------------------------------
#> phi is not specified in initial values.
#> Setting initial value to random values from the prior distribution
#> lambda is not specified in initial values.
#> Setting initial values of the lower triangle to random values from a standard normal
#> w is not specified in initial values.
#> Setting initial value to 0
#> ----------------------------------------
#> Building the neighbor list
#> ----------------------------------------
#> ----------------------------------------
#> Building the neighbors of neighbors list
#> ----------------------------------------
#> ----------------------------------------
#> Model description
#> ----------------------------------------
#> Spatial Factor NNGP Multispecies Occupancy Model with Polya-Gamma latent
#> variable fit with 75 sites and 6 species.
#>
#> Samples per chain: 50 (2 batches of length 25)
#> Burn-in: 0
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 50
#>
#> Number of spatially-varying coefficients: 3
#> Using the spherical spatial correlation model.
#>
#> Using 2 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: 2 of 2, 100.00%
summary(out)
#>
#> Call:
#> svcMsPGOcc(occ.formula = ~occ.cov.1 + occ.cov.2 + occ.cov.3 +
#> occ.cov.4, det.formula = ~det.cov.1 + det.cov.2, data = data.list,
#> inits = inits.list, priors = prior.list, tuning = tuning.list,
#> svc.cols = svc.cols, cov.model = "spherical", NNGP = TRUE,
#> n.neighbors = 5, search.type = "cb", std.by.sp = TRUE, n.factors = n.factors,
#> n.batch = n.batch, batch.length = batch.length, accept.rate = 0.43,
#> n.omp.threads = 1, verbose = TRUE, n.report = 10, n.burn = n.burn,
#> n.thin = n.thin, n.chains = 1)
#>
#> Samples per Chain: 50
#> Burn-in: 0
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 50
#> Run Time (min): 0.0033
#>
#> ----------------------------------------
#> Community Level
#> ----------------------------------------
#> Occurrence Means (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.3865 0.5685 -1.1749 0.4292 1.2276 NA 50
#> occ.cov.1 0.0081 0.5905 -1.1959 0.0432 1.1084 NA 173
#> occ.cov.2 0.7362 0.3440 -0.1158 0.7717 1.3399 NA 10
#> occ.cov.3 0.0562 0.2659 -0.4958 0.0354 0.4986 NA 11
#> occ.cov.4 0.8627 0.3776 0.2992 0.8223 1.5092 NA 33
#>
#> Occurrence Variances (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 1.3177 1.3943 0.1741 0.7425 4.1792 NA 18
#> occ.cov.1 3.1192 3.4246 0.1013 2.2301 13.7831 NA 26
#> occ.cov.2 0.3586 0.6218 0.0511 0.2246 1.0391 NA 50
#> occ.cov.3 0.2961 0.2932 0.0393 0.2037 1.1387 NA 19
#> occ.cov.4 0.6849 0.5199 0.2031 0.5123 1.9494 NA 23
#>
#> Detection Means (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) -0.3338 0.5077 -1.4572 -0.2468 0.4008 NA 32
#> det.cov.1 1.1351 0.4890 0.2226 1.0978 2.1360 NA 23
#> det.cov.2 -0.3246 0.5099 -1.1707 -0.3391 0.5401 NA 50
#>
#> Detection Variances (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.9784 1.1061 0.1420 0.7099 3.4060 NA 50
#> det.cov.1 1.4190 1.7630 0.0566 0.6807 5.4301 NA 13
#> det.cov.2 2.1039 2.1854 0.2831 1.3321 7.6769 NA 50
#>
#> ----------------------------------------
#> Species Level
#> ----------------------------------------
#> Occurrence (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept)-sp1 0.1204 0.4108 -0.8129 0.1333 0.8772 NA 12
#> (Intercept)-sp2 0.5152 0.3386 -0.1270 0.5078 1.0796 NA 23
#> (Intercept)-sp3 1.2984 0.4233 0.7146 1.2412 2.1715 NA 17
#> (Intercept)-sp4 0.5981 0.5428 -0.2577 0.5200 1.5575 NA 5
#> (Intercept)-sp5 0.7718 0.4711 -0.0883 0.8728 1.4816 NA 9
#> (Intercept)-sp6 -0.7744 0.4436 -1.6482 -0.7071 -0.1762 NA 9
#> occ.cov.1-sp1 0.2998 0.4075 -0.3943 0.2956 1.2428 NA 13
#> occ.cov.1-sp2 2.2276 0.8809 0.4118 2.2859 3.4414 NA 6
#> occ.cov.1-sp3 0.8633 0.5466 0.0243 0.9007 1.8449 NA 12
#> occ.cov.1-sp4 -1.1789 0.7235 -2.5228 -1.2085 -0.0175 NA 5
#> occ.cov.1-sp5 -0.2925 0.5078 -1.1791 -0.3295 0.5847 NA 13
#> occ.cov.1-sp6 -1.0185 0.5218 -1.9747 -0.9902 -0.0561 NA 9
#> occ.cov.2-sp1 0.6744 0.2852 0.1269 0.7041 1.1580 NA 25
#> occ.cov.2-sp2 0.8395 0.3460 0.0787 0.8597 1.3587 NA 30
#> occ.cov.2-sp3 0.4144 0.4998 -0.5444 0.4081 1.3089 NA 6
#> occ.cov.2-sp4 0.5985 0.4612 -0.5446 0.6236 1.3293 NA 19
#> occ.cov.2-sp5 1.1814 0.4116 0.4731 1.2444 1.9073 NA 9
#> occ.cov.2-sp6 0.5817 0.4090 -0.1759 0.6052 1.3318 NA 16
#> occ.cov.3-sp1 0.1635 0.2813 -0.3860 0.1352 0.7058 NA 21
#> occ.cov.3-sp2 -0.2556 0.2746 -0.7935 -0.1994 0.2446 NA 27
#> occ.cov.3-sp3 -0.3107 0.3698 -0.9376 -0.2785 0.3672 NA 19
#> occ.cov.3-sp4 0.6446 0.4050 0.0485 0.6618 1.5711 NA 7
#> occ.cov.3-sp5 -0.0053 0.2979 -0.5681 -0.0031 0.6136 NA 16
#> occ.cov.3-sp6 0.1729 0.2715 -0.3626 0.1452 0.8022 NA 14
#> occ.cov.4-sp1 1.6203 0.4602 0.8826 1.6058 2.5588 NA 20
#> occ.cov.4-sp2 0.9906 0.5377 0.1522 0.8947 1.9813 NA 11
#> occ.cov.4-sp3 -0.1165 0.4216 -0.9665 -0.1469 0.7349 NA 11
#> occ.cov.4-sp4 1.0866 0.4027 0.4983 1.0434 1.9043 NA 19
#> occ.cov.4-sp5 0.7303 0.4934 -0.2793 0.7929 1.5352 NA 9
#> occ.cov.4-sp6 0.8864 0.2991 0.4276 0.8976 1.4710 NA 27
#>
#> Detection (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept)-sp1 0.8278 0.3256 0.1824 0.8555 1.4689 NA 16
#> (Intercept)-sp2 0.0943 0.2817 -0.4700 0.1230 0.5269 NA 14
#> (Intercept)-sp3 0.3342 0.2001 -0.0304 0.3151 0.7154 NA 50
#> (Intercept)-sp4 -1.0454 0.2936 -1.5948 -1.0048 -0.5161 NA 17
#> (Intercept)-sp5 -0.8061 0.2454 -1.1824 -0.8404 -0.3858 NA 10
#> (Intercept)-sp6 -0.6116 0.2909 -1.1882 -0.6198 -0.1343 NA 22
#> det.cov.1-sp1 1.0036 0.3055 0.5914 0.9636 1.5820 NA 8
#> det.cov.1-sp2 2.4081 0.7330 1.2315 2.2326 3.8627 NA 6
#> det.cov.1-sp3 0.4143 0.1909 0.0993 0.4279 0.8450 NA 33
#> det.cov.1-sp4 1.6223 0.4313 0.8609 1.6472 2.2960 NA 7
#> det.cov.1-sp5 1.0948 0.2096 0.6819 1.0998 1.4972 NA 25
#> det.cov.1-sp6 1.2477 0.3431 0.5479 1.3057 1.8199 NA 21
#> det.cov.2-sp1 -0.6427 0.2398 -1.0699 -0.6205 -0.2813 NA 38
#> det.cov.2-sp2 -1.8715 0.5901 -3.1050 -1.7665 -1.0658 NA 9
#> det.cov.2-sp3 -0.9136 0.2023 -1.3211 -0.8808 -0.5774 NA 50
#> det.cov.2-sp4 -0.2174 0.2609 -0.7359 -0.1965 0.2730 NA 28
#> det.cov.2-sp5 0.6222 0.2505 0.1696 0.5835 1.0950 NA 29
#> det.cov.2-sp6 1.0674 0.4100 0.4339 1.0182 1.9062 NA 12
#>
#> ----------------------------------------
#> Spatial Covariance
#> ----------------------------------------
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> phi-1-(Intercept) 16.6851 5.3523 8.1941 16.1706 24.5452 NA 10
#> phi-2-(Intercept) 18.6767 4.5936 10.0707 18.5800 25.3736 NA 25
#> phi-1-occ.cov.1 15.6544 8.4278 3.7932 16.6590 27.7249 NA 4
#> phi-2-occ.cov.1 11.7298 4.8515 5.2252 11.7010 21.1147 NA 16
#> phi-1-occ.cov.2 10.4756 3.6043 5.9287 9.8572 18.3046 NA 13
#> phi-2-occ.cov.2 14.6710 4.3363 8.5785 13.8155 23.0049 NA 30
# Predict at new locations ------------------------------------------------
out.pred <- predict(out, X.0, coords.0, verbose = FALSE)
# Get SVC samples for each species at prediction locations
svc.samples <- getSVCSamples(out, out.pred)