Function for prediction at new locations for latent factor multi-species hierarchical distance sampling models
predict.lfMsDS.RdThe function predict collects posterior predictive samples for a set of new locations given an object of class `lfMsDS`. Prediction is possible for both the latent abundance state as well as detection.
Usage
# S3 method for lfMsDS
predict(object, X.0, coords.0, ignore.RE = FALSE,
type = 'abundance', include.w = TRUE, ...)Arguments
- object
an object of class lfMsDS
- 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 abundance (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 inlfMsDS. Columns should correspond to the order of how covariates were specified in the corresponding formula argument oflfMsDS. Column names must match the names of the variables used to fit the model (for the intercept, use'(Intercept)').- 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.
- type
a quoted keyword indicating what type of prediction to produce. Valid keywords are 'abundance' to predict expected abundance and latent abundance values (this is the default), or 'detection' to predict detection probability given new values of detection covariates.
- include.w
a logical value used to indicate whether the latent random effects should be included in the predictions. By default, this is set to
TRUE. If set toFALSE, predictions are given using the covariates and any unstructured random effects in the model. IfFALSE, thecoords.0argument is not required.- ...
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
Jeffrey W. Doser doserjef@msu.edu,
Value
A list object of class predict.lfMsDS. When type = 'abundance', the list consists of:
- mu.0.samples
a three-dimensional array of posterior predictive samples for the expected abundance values, or expected abundance values per unit area (i.e., density) values when an offset was used when fitting the model with
lfMsDS().- N.0.samples
a three-dimensional array of posterior predictive samples for the latent abundance values. These will be in the same units as
mu.0.samples.
When type = 'detection', the list consists of:
- sigma.0.samples
a three-dimensional array of posterior predictive samples for sigma (the parameter controlling detection probability).
The return object will include additional objects used for standard extractor functions.
Examples
set.seed(210)
J.x <- 10
J.y <- 10
J <- J.x * J.y
# Number of distance bins from which to simulate data.
n.bins <- 5
# Length of each bin. This should be of length n.bins
bin.width <- c(.10, .10, .20, .3, .1)
# Number of species
n.sp <- 5
# Community-level abundance coefficients
beta.mean <- c(-1, 0.2, 0.3, -0.2)
p.abund <- length(beta.mean)
tau.sq.beta <- c(0.2, 0.3, 0.5, 0.4)
# Detection coefficients
alpha.mean <- c(-1.0, -0.3)
p.det <- length(alpha.mean)
tau.sq.alpha <- c(0.1, 0.2)
# Detection decay function
det.func <- 'halfnormal'
mu.RE <- list()
p.RE <- list()
# Draw species-level effects from community means.
beta <- matrix(NA, nrow = n.sp, ncol = p.abund)
alpha <- matrix(NA, nrow = n.sp, ncol = p.det)
for (i in 1:p.abund) {
beta[, i] <- rnorm(n.sp, beta.mean[i], sqrt(tau.sq.beta[i]))
}
for (i in 1:p.det) {
alpha[, i] <- rnorm(n.sp, alpha.mean[i], sqrt(tau.sq.alpha[i]))
}
sp <- FALSE
family <- 'NB'
kappa <- runif(n.sp, 0.3, 3)
offset <- pi * .8^2
transect <- 'line'
factor.model <- TRUE
n.factors <- 3
dat <- simMsDS(J.x = J.x, J.y = J.y, n.bins = n.bins, bin.width = bin.width,
n.sp = n.sp, beta = beta, alpha = alpha, det.func = det.func, kappa = kappa,
mu.RE = mu.RE, p.RE = p.RE, sp = sp, cov.model = cov.model,
sigma.sq = sigma.sq, phi = phi, nu = nu, family = family,
offset = offset, transect = transect, factor.model = factor.model,
n.factors = n.factors)
# 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, ]
# Prediction covariates
X.0 <- dat$X[pred.indx, ]
# Detection covariates
X.p <- dat$X.p[-pred.indx, , drop = FALSE]
X.p.0 <- dat$X.p[pred.indx, , drop = FALSE]
coords <- as.matrix(dat$coords[-pred.indx, ])
coords.0 <- as.matrix(dat$coords[pred.indx, ])
dist.breaks <- dat$dist.breaks
covs <- cbind(X, X.p)
colnames(covs) <- c('int.abund', 'abund.cov.1', 'abund.cov.2', 'abund.cov.3',
'int.det', 'det.cov.1')
data.list <- list(y = y,
covs = covs,
dist.breaks = dist.breaks,
coords = coords,
offset = offset)
# Priors
prior.list <- list(beta.comm.normal = list(mean = 0, var = 10),
alpha.comm.normal = list(mean = 0,
var = 10),
kappa.unif = list(0, 100),
tau.sq.beta.ig = list(a = 0.1, b = 0.1),
tau.sq.alpha.ig = list(a = 0.1, b = 0.1))
# Starting values
inits.list <- list(alpha.comm = 0, beta.comm = 0, beta = 0,
alpha = 0, kappa = 1)
tuning <- list(beta = 0.1, alpha = 0.1, beta.star = 0.3, alpha.star = 0.1,
kappa = 0.8, lambda = 1, w = 1)
n.batch <- 4
batch.length <- 25
n.burn <- 0
n.thin <- 1
n.chains <- 1
out <- lfMsDS(abund.formula = ~ abund.cov.1 + abund.cov.2 + abund.cov.3,
det.formula = ~ det.cov.1,
data = data.list,
n.batch = n.batch,
batch.length = batch.length,
inits = inits.list,
family = 'Poisson',
det.func = 'halfnormal',
transect = transect,
tuning = tuning,
n.factors = n.factors,
priors = prior.list,
accept.rate = 0.43,
n.omp.threads = 1,
verbose = TRUE,
n.report = 10,
n.burn = n.burn,
n.thin = n.thin,
n.chains = n.chains)
#> ----------------------------------------
#> Preparing to run the model
#> ----------------------------------------
#> N is not specified in initial values.
#> Setting initial values based on observed data
#> tau.sq.beta is not specified in initial values.
#> Setting initial values to random values between 0.05 and 1
#> tau.sq.alpha is not specified in initial values.
#> Setting to initial values to random values between 0.05 and 1
#> lambda is not specified in initial values.
#> Setting initial values of the lower triangle to 0
#> w is not specified in initial values.
#> Setting initial value to 0
#> ----------------------------------------
#> Model description
#> ----------------------------------------
#> Latent Factor Multi-species Poisson HDS model with 75 sites and 5 species.
#>
#> Samples per Chain: 100 (4 batches of length 25)
#> Burn-in: 0
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 100
#>
#> Using 3 latent factors.
#>
#> Source compiled with OpenMP support and model fit using 1 thread(s).
#>
#> Adaptive Metropolis with target acceptance rate: 43.0
#> ----------------------------------------
#> Chain 1
#> ----------------------------------------
#> Sampling ...
#> Batch: 4 of 4, 100.00%
summary(out, level = 'community')
#>
#> Call:
#> lfMsDS(abund.formula = ~abund.cov.1 + abund.cov.2 + abund.cov.3,
#> det.formula = ~det.cov.1, data = data.list, inits = inits.list,
#> priors = prior.list, tuning = tuning, n.factors = n.factors,
#> n.batch = n.batch, batch.length = batch.length, accept.rate = 0.43,
#> family = "Poisson", transect = transect, det.func = "halfnormal",
#> n.omp.threads = 1, verbose = TRUE, n.report = 10, n.burn = n.burn,
#> n.thin = n.thin, n.chains = n.chains)
#>
#> Samples per Chain: 100
#> Burn-in: 0
#> Thinning Rate: 1
#> Number of Chains: 1
#> Total Posterior Samples: 100
#> Run Time (min): 0.0045
#>
#> ----------------------------------------
#> Community Level
#> ----------------------------------------
#> Abundance Means (log scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) -0.5817 0.3760 -1.3623 -0.5692 0.1000 NA 5
#> abund.cov.1 0.2638 0.2269 -0.0737 0.2220 0.7656 NA 74
#> abund.cov.2 0.2451 0.4218 -0.3946 0.1716 1.2111 NA 15
#> abund.cov.3 -0.1690 0.2298 -0.7257 -0.1516 0.2448 NA 100
#>
#> Abundance Variances (log scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.4367 0.4444 0.0663 0.2740 1.4150 NA 100
#> abund.cov.1 0.2166 0.2234 0.0377 0.1372 0.9639 NA 54
#> abund.cov.2 0.7997 0.8981 0.1142 0.5395 2.8159 NA 39
#> abund.cov.3 0.2571 0.3018 0.0431 0.1558 0.8382 NA 62
#>
#> Detection Means (log scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) -0.6379 0.3808 -1.1463 -0.7362 0.1397 NA 4
#> det.cov.1 -0.4689 0.3717 -1.3061 -0.4183 0.1813 NA 19
#>
#> Detection Variances (log scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) 0.1188 0.1104 0.0226 0.0798 0.3751 NA 100
#> det.cov.1 0.4085 0.4437 0.0599 0.2707 1.6474 NA 67
# Predict at new locations ------------------------------------------------
colnames(X.0) <- c('intercept', 'abund.cov.1', 'abund.cov.2', 'abund.cov.3')
out.pred <- predict(out, X.0, coords.0)
str(out.pred)
#> List of 3
#> $ mu.0.samples: num [1:100, 1:5, 1:25] 0.892 0.332 0.617 0.402 0.734 ...
#> $ N.0.samples : int [1:100, 1:5, 1:25] 0 1 1 1 0 0 1 0 1 7 ...
#> $ call : language predict.lfMsNMix(object = object, X.0 = X.0, coords.0 = coords.0, ignore.RE = ignore.RE, type = "abundance",| __truncated__
#> - attr(*, "class")= chr "predict.lfMsDS"