Function for prediction at new locations for latent factor multi-species occupancy models
predict.lfMsPGOcc.RdThe function predict collects posterior predictive samples for a set of new locations given an object of class `lfMsPGOcc`. Prediction is possible for both the latent occupancy state as well as detection.
Usage
# S3 method for lfMsPGOcc
predict(object, X.0, coords.0,
ignore.RE = FALSE, type = 'occupancy', ...)Arguments
- object
an object of class lfMsPGOcc
- 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 inlfMsPGOcc. Columns should correspond to the order of how covariates were specified in the corresponding formula argument oflfMsPGOcc. Column names of the random effects must match the name of the random effects, if specified in the corresponding formula argument oflfMsPGOcc.- coords.0
the spatial coordinates corresponding to
X.0. Note thatspOccupancyassumes coordinates are specified in a projected coordinate system.- ignore.RE
a logical value indicating whether to include unstructured random effects for prediction. If TRUE, random effects will be ignored and prediction will only use the fixed effects. If FALSE, random effects will be included in the prediction for both observed and unobserved levels of the random effect.
- ...
currently no additional arguments
- 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
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
A list object of class predict.lfMsPGOcc. 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 factors.
When type = 'detection', the list consists of:
- p.0.samples
a three-dimensional array of posterior predictive samples for the detection probability values.
The return object will include additional objects used for standard extractor functions.
Examples
set.seed(400)
J.x <- 8
J.y <- 8
J <- J.x * J.y
n.rep<- sample(2:4, size = J, replace = TRUE)
N <- 6
# Community-level covariate effects
# Occurrence
beta.mean <- c(0.2, 0.5)
p.occ <- length(beta.mean)
tau.sq.beta <- c(0.6, 0.3)
# Detection
alpha.mean <- c(0.5, 0.2, -0.1)
tau.sq.alpha <- c(0.2, 0.3, 1)
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
dat <- simMsOcc(J.x = J.x, J.y = J.y, n.rep = n.rep, N = N, beta = beta, alpha = alpha,
sp = FALSE, factor.model = TRUE, n.factors = n.factors)
n.samples <- 5000
# 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, ]
# Spatial coordinates
coords <- dat$coords[-pred.indx, ]
# Detection covariates
X.p <- dat$X.p[-pred.indx, , ]
# Prediction values
X.0 <- dat$X[pred.indx, ]
psi.0 <- dat$psi[, pred.indx]
coords.0 <- dat$coords[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)
# Occupancy initial values
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))
# Initial 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,
lambda = lambda.inits,
z = apply(y, c(1, 2), max, na.rm = TRUE))
out <- lfMsPGOcc(occ.formula = ~ occ.cov,
det.formula = ~ det.cov.1 + det.cov.2,
data = data.list,
inits = inits.list,
n.samples = n.samples,
n.factors = 3,
priors = prior.list,
n.omp.threads = 1,
verbose = TRUE,
n.report = 1000,
n.burn = 4000)
#> ----------------------------------------
#> Preparing to run the model
#> ----------------------------------------
#> ----------------------------------------
#> Model description
#> ----------------------------------------
#> Latent Factor Multi-species Occupancy Model with Polya-Gamma latent
#> variable fit with 48 sites and 6 species.
#>
#> Samples per Chain: 5000
#> Burn-in: 4000
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 1000
#>
#> Using 3 latent factors.
#>
#> Source compiled with OpenMP support and model fit using 1 thread(s).
#>
#> ----------------------------------------
#> Chain 1
#> ----------------------------------------
#> Sampling ...
#> Sampled: 1000 of 5000, 20.00%
#> -------------------------------------------------
#> Sampled: 2000 of 5000, 40.00%
#> -------------------------------------------------
#> Sampled: 3000 of 5000, 60.00%
#> -------------------------------------------------
#> Sampled: 4000 of 5000, 80.00%
#> -------------------------------------------------
#> Sampled: 5000 of 5000, 100.00%
summary(out, level = 'community')
#>
#> Call:
#> lfMsPGOcc(occ.formula = ~occ.cov, det.formula = ~det.cov.1 +
#> det.cov.2, data = data.list, inits = inits.list, priors = prior.list,
#> n.factors = 3, n.samples = n.samples, n.omp.threads = 1,
#> verbose = TRUE, n.report = 1000, n.burn = 4000)
#>
#> Samples per Chain: 5000
#> Burn-in: 4000
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 1000
#> Run Time (min): 0.0238
#>
#> ----------------------------------------
#> Community Level
#> ----------------------------------------
#> Occurrence Means (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) -0.2442 0.7795 -1.8753 -0.2200 1.3575 NA 629
#> occ.cov 0.2642 0.3975 -0.5575 0.2787 0.9767 NA 243
#>
#> Occurrence Variances (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 4.818 5.4869 0.8559 3.2926 19.8592 NA 428
#> occ.cov 0.584 1.2156 0.0449 0.2712 3.0153 NA 155
#>
#> Detection Means (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.2074 0.3044 -0.4415 0.2153 0.7622 NA 232
#> det.cov.1 0.3696 0.3077 -0.2459 0.3652 0.9771 NA 542
#> det.cov.2 -0.4822 0.5534 -1.6597 -0.4697 0.6316 NA 778
#>
#> Detection Variances (logit scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.4239 0.8239 0.0461 0.2225 1.9411 NA 419
#> det.cov.1 0.4695 0.6115 0.0607 0.3022 1.8249 NA 559
#> det.cov.2 2.0620 2.7890 0.2227 1.2241 9.4208 NA 329
# Predict at new locations ------------------------------------------------
out.pred <- predict(out, X.0, coords.0)