The function sfJSDM fits a spatially-explicit joint species distribution model. This model does not explicitly account for imperfect detection (see sfMsPGOcc()). We use Polya-Gamma latent variables and a spatial factor modeling approach. Currently, models are implemented using a Nearest Neighbor Gaussian Process.
sfJSDM(formula, data, inits, priors, tuning,
cov.model = 'exponential', NNGP = TRUE,
n.neighbors = 15, search.type = 'cb',
std.by.sp = FALSE, n.factors, n.batch,
batch.length, accept.rate = 0.43, n.omp.threads = 1,
verbose = TRUE, n.report = 100,
n.burn = round(.10 * n.batch * batch.length), n.thin = 1,
n.chains = 1, k.fold,
k.fold.threads = 1, k.fold.seed = 100,
k.fold.only = FALSE, monitors, keep.only.mean.95,
shared.spatial = FALSE, ...)An object of class sfJSDM that is a list comprised of:
a coda object of posterior samples
for the community level occurrence regression coefficients.
a coda object of posterior samples
for the occurrence community variance parameters.
a coda object of posterior samples
for the species level occurrence regression coefficients.
a coda object of posterior samples
for the species level correlation parameters.
a coda object of posterior samples
for the latent spatial factor loadings.
a three-dimensional array of posterior samples for the latent occurrence probability values for each species.
a three-dimensional array of posterior samples for
the latent spatial random effects for each latent factor. Array
dimensions correspond to MCMC sample, latent factor, and site.
If shared.spatial = TRUE, this is still returned as a
three-dimensional array where the first dimension is MCMC sample,
second dimension is 1, and third dimension is site.
a coda object of posterior samples
for variances of random intercepts included in the occurrence portion
of the model. Only included if random intercepts are specified in
formula.
a coda object of posterior samples
for the occurrence random effects. Only included if random intercepts
are specified in formula.
a three-dimensional array of posterior samples for the likelihood value associated with each site and species. Used for calculating WAIC.
a list of Gelman-Rubin diagnostic values for some of the model parameters.
a list of effective sample sizes for some of the model parameters.
MCMC sampler execution time reported using proc.time().
vector of scoring rules (deviance) from k-fold cross-validation.
A separate value is reported for each species.
Only included if k.fold is specified in function call.
The return object will include additional objects used for
subsequent prediction and/or model fit evaluation. Note that detection probability
estimated values are not included in the model object, but can be extracted
using fitted().
a symbolic description of the model to be fit for the model using R's model syntax. Only right-hand side of formula is specified. See example below. Random intercepts are allowed using lme4 syntax (Bates et al. 2015).
a list containing data necessary for model fitting.
Valid tags are y, covs, coords, range.ind, and grid.index. y
is a two-dimensional array with first dimension equal to the number
of species and second dimension equal to the number of sites. Note how this differs
from other spOccupancy functions in that y does not have any
replicate surveys. This is because sfJSDM does not account for imperfect
detection. covs is a matrix or data frame containing the variables
used in the model, with \(J\) rows for
each column (variable). coords is a matrix of the observation coordinates used
to estimate the SVCs for each site. coords has two columns for the
easting and northing coordinate, respectively. Typically, each site in the data
set will have it's own coordinate, such that coords is a \(J \times 2\)
matrix and grid.index should not be specified.
If you desire to estimate SVCs at some larger spatial level,
e.g., if points fall within grid cells and you want to estimate an SVC for
each grid cell instead of each point, coords can be specified as the coordinate for
each grid cell. In such a case, grid.index is an indexing vector of length J, where each
value of grid.index indicates the corresponding row in coords that the given
site corresponds to. Note that spOccupancy assumes coordinates are specified
in a projected coordinate system.
range.ind is a matrix with rows corresponding to species and columns
corresponding to sites, with each element taking value 1 if that site is
within the range of the corresponding species and 0 if it is outside of the
range. This matrix is not required, but it can be helpful to restrict the
modeled area for each individual species to be within the realistic range
of locations for that species when estimating the model parameters.
a list with each tag corresponding to a parameter name.
Valid tags are beta.comm, beta, tau.sq.beta,
phi, lambda, sigma.sq.psi, and nu.
nu is only specified if cov.model = "matern".
sigma.sq.psi is only specified if
random intercepts are included in formula. The value portion of each tag is
the parameter's initial value. See priors description for definition
of each parameter name. Additionally, the tag fix can be set to TRUE
to fix the starting values across all chains. If fix is not specified
(the default), starting values are varied randomly across chains.
a list with each tag corresponding to a parameter name.
Valid tags are beta.comm.normal, tau.sq.beta.ig, phi.unif,
nu.unif, and sigma.sq.psi.ig. Community-level occurrence
(beta.comm) regression coefficients are assumed to follow a
normal distribution. The hyperparameters of the normal distribution
are passed as a list of length two with the first and second elements
corresponding to the mean and variance of the normal distribution,
which are each specified as vectors of length equal to the number of
coefficients to be estimated or of length one if priors are the same for
all coefficients. If not specified, prior means are set
to 0 and prior variances set to 2.73. Community-level variance parameters
(tau.sq.beta) are assumed to follow an
inverse Gamma distribution. The hyperparameters of
the inverse gamma distribution are passed as a list of length two with
the first and second elements corresponding to the shape and scale parameters,
which are each specified as vectors of length equal to the number of
coefficients to be estimated or a single value if priors are the same for all
parameters. If not specified, prior shape and scale
parameters are set to 0.1. If desired, the species-specific regression coefficients
(beta) can also be estimated indepdendently by specifying the
tag independent.betas = TRUE. If specified, this will not estimate species-specific
coefficients as random effects from a common-community-level distribution, and rather
the values of beta.comm and tau.sq.beta will be fixed at the
specified initial values. This is equivalent to specifying a Gaussian, independent
prior for each of the species-specific effects.
The spatial factor model fits n.factors independent
spatial processes. The spatial decay phi and smoothness nu parameters
for each latent factor are assumed to follow Uniform distributions.
The hyperparameters of the Uniform are passed as a list with two elements,
with both elements being vectors of length n.factors corresponding to the lower and
upper support, respectively, or as a single value if the same value is assigned
for all factors. The priors for the factor loadings matrix lambda are fixed
following the standard spatial factor model to ensure parameter
identifiability (Christensen and Amemlya 2002). The
upper triangular elements of the N x n.factors matrix are fixed at 0 and the
diagonal elements are fixed at 1. The lower triangular elements are assigned a
standard normal prior (i.e., mean 0 and variance 1).
sigma.sq.psi is the random effect variance for any random effects, and is assumed
to follow an inverse Gamma distribution. The hyperparameters of the inverse-Gamma distribution
are passed as a list of length two with first and second elements corresponding to the shape
and scale parameters, respectively, which are each specified as vectors of length equal to
the number of random intercepts or of length one if priors are the same for all random
effect variances.
a list with each tag corresponding to a parameter
name. Valid tags are phi and nu. The value portion of each
tag defines the initial variance of the adaptive sampler. We assume the
initial variance of the adaptive sampler is the same for each species,
although the adaptive sampler will adjust the tuning variances separately
for each species. See Roberts and Rosenthal (2009) for details.
a quoted keyword that specifies the covariance
function used to model the spatial dependence structure among the
observations. Supported covariance model key words are:
"exponential", "matern", "spherical", and
"gaussian".
if TRUE, model is fit with an NNGP. If FALSE,
a full Gaussian process is used. See Datta et al. (2016) and
Finley et al. (2019) for more information. For spatial factor models, only
NNGP = TRUE is currently supported.
number of neighbors used in the NNGP. Only used if
NNGP = TRUE. Datta et al. (2016) showed that 15 neighbors is usually
sufficient, but that as few as 5 neighbors can be adequate for certain data
sets, which can lead to even greater decreases in run time. We recommend
starting with 15 neighbors (the default) and if additional gains in computation
time are desired, subsequently compare the results with a smaller number
of neighbors using WAIC or k-fold cross-validation.
a quoted keyword that specifies the type of nearest
neighbor search algorithm. Supported method key words are: "cb" and
"brute". The "cb" should generally be much
faster. If locations do not have identical coordinate values on
the axis used for the nearest neighbor ordering then "cb"
and "brute" should produce identical neighbor sets.
However, if there are identical coordinate values on the axis used
for nearest neighbor ordering, then "cb" and "brute"
might produce different, but equally valid, neighbor sets,
e.g., if data are on a grid.
a logical value indicating whether the covariates are standardized
separately for each species within the corresponding range for each species (TRUE)
or not (FALSE). Note that if range.ind is specified in data.list,
this will result in the covariates being standardized differently for each species
based on the sites where range.ind == 1 for that given species. If range.ind is not specified
and std.by.sp = TRUE, this will simply be equivalent to standardizing
the covariates across all locations prior to fitting the model. Note that the covariates
in formula should still be standardized across all locations. This can be done
either outside the function, or can be done by specifying scale() in the model formula
around the continuous covariates.
the number of factors to use in the spatial factor model approach. Typically, the number of factors is set to be small (e.g., 4-5) relative to the total number of species in the community, which will lead to substantial decreases in computation time. However, the value can be anywhere between 1 and N (the number of species in the community).
the number of MCMC batches in each chain to run for the Adaptive MCMC sampler. See Roberts and Rosenthal (2009) for details.
the length of each MCMC batch to run for the Adaptive MCMC sampler. See Roberts and Rosenthal (2009) for details.
target acceptance rate for Adaptive MCMC. Defaul is 0.43. See Roberts and Rosenthal (2009) for details.
a positive integer indicating
the number of threads to use for SMP parallel processing within chains. 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.
if TRUE, messages about data preparation,
model specification, and progress of the sampler are printed to the screen.
Otherwise, no messages are printed.
the interval to report Metropolis sampler acceptance and MCMC progress. Note this is specified in terms of batches and not overall samples for spatial models.
the number of samples out of the total n.samples to
discard as burn-in for each chain. By default, the first 10% of samples is discarded.
the thinning interval for collection of MCMC samples. The
thinning occurs after the n.burn samples are discarded. Default
value is set to 1.
the number of chains to run in sequence.
specifies the number of k folds for cross-validation.
If not specified as an argument, then cross-validation is not performed
and k.fold.threads and k.fold.seed are ignored. In k-fold
cross-validation, the data specified in data is randomly
partitioned into k equal sized subsamples. Of the k subsamples,
k - 1 subsamples are used to fit the model and the remaining k
samples are used for prediction. The cross-validation process is repeated
k times (the folds). As a scoring rule, we use the model deviance
as described in Hooten and Hobbs (2015). Cross-validation is performed
after the full model is fit using all the data. Cross-validation results
are reported in the k.fold.deviance object in the return list.
number of threads to use for cross-validation. If
k.fold.threads > 1 parallel processing is accomplished using the
foreach and doParallel packages. Ignored if k.fold
is not specified.
seed used to split data set into k.fold parts
for k-fold cross-validation. Ignored if k.fold is not specified.
a logical value indicating whether to only perform
cross-validation (TRUE) or perform cross-validation after fitting
the full model (FALSE). Default value is FALSE.
a character vector used to indicate if only a subset of the model
model parameters are desired to be monitored. If posterior samples of all parameters
are desired, then don't specify the argument (this is the default). When working
with a large number of species and/or sites, the full model object can be quite
large, and so this argument can be used to only return samples of specific
parameters to help reduce the size of this resulting object. Valid tags include
beta.comm, tau.sq.beta, beta, z, psi, lambda,
theta, w, like (used for WAIC calculation),
beta.star, sigma.sq.psi. Note that if all parameters are not returned,
subsequent functions that require the model object may not work. We only recommend
specifying this option when working with large data sets (e.g., > 100 species and/or
> 10,000 sites).
not currently supported.
a logical value used to specify whether a common spatial process
should be estimated for all species instead of the factor modeling approach. If true,
a spatial variance parameter sigma.sq is estimated for the model, which can
be specified in the initial values and prior distributions (sigma.sq.ig).
currently no additional arguments
Jeffrey W. Doser doserjef@msu.edu,
Andrew O. Finley finleya@msu.edu
Datta, A., S. Banerjee, A.O. Finley, and A.E. Gelfand. (2016) Hierarchical Nearest-Neighbor Gaussian process models for large geostatistical datasets. Journal of the American Statistical Association, tools:::Rd_expr_doi("10.1080/01621459.2015.1044091").
Finley, A.O., A. Datta, B.D. Cook, D.C. Morton, H.E. Andersen, and S. Banerjee. (2019) Efficient algorithms for Bayesian Nearest Neighbor Gaussian Processes. Journal of Computational and Graphical Statistics, tools:::Rd_expr_doi("10.1080/10618600.2018.1537924").
Finley, A. O., Datta, A., and Banerjee, S. (2020). spNNGP R package for nearest neighbor Gaussian process models. arXiv preprint arXiv:2001.09111.
Polson, N.G., J.G. Scott, and J. Windle. (2013) Bayesian Inference for Logistic Models Using Polya-Gamma Latent Variables. Journal of the American Statistical Association, 108:1339-1349.
Roberts, G.O. and Rosenthal J.S. (2009) Examples of adaptive MCMC. Journal of Computational and Graphical Statistics, 18(2):349-367.
Bates, Douglas, Martin Maechler, Ben Bolker, Steve Walker (2015). Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software, 67(1), 1-48. tools:::Rd_expr_doi("10.18637/jss.v067.i01").
Hooten, M. B., and Hobbs, N. T. (2015). A guide to Bayesian model selection for ecologists. Ecological Monographs, 85(1), 3-28.
Christensen, W. F., and Amemiya, Y. (2002). Latent variable analysis of multivariate spatial data. Journal of the American Statistical Association, 97(457), 302-317.
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)
p.occ <- length(beta.mean)
tau.sq.beta <- c(0.6)
# Detection
alpha.mean <- c(0)
tau.sq.alpha <- c(1)
p.det <- length(alpha.mean)
# 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]))
}
alpha.true <- alpha
n.factors <- 3
phi <- rep(3 / .7, n.factors)
sigma.sq <- rep(2, n.factors)
nu <- rep(2, n.factors)
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, sp = TRUE, sigma.sq = sigma.sq,
phi = phi, nu = nu, cov.model = 'matern', factor.model = TRUE,
n.factors = n.factors)
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]
coords <- as.matrix(dat$coords[-pred.indx, , drop = FALSE])
# Prediction covariates
X.0 <- dat$X[pred.indx, , drop = FALSE]
coords.0 <- as.matrix(dat$coords[pred.indx, , drop = FALSE])
# Detection covariates
X.p <- dat$X.p[-pred.indx, , , drop = FALSE]
y <- apply(y, c(1, 2), max, na.rm = TRUE)
data.list <- list(y = y, coords = coords)
# Priors
prior.list <- list(beta.comm.normal = list(mean = 0, var = 2.72),
tau.sq.beta.ig = list(a = 0.1, b = 0.1),
nu.unif = list(0.5, 2.5))
# Starting values
inits.list <- list(beta.comm = 0,
beta = 0,
fix = TRUE,
tau.sq.beta = 1)
# Tuning
tuning.list <- list(phi = 1, nu = 0.25)
batch.length <- 25
n.batch <- 5
n.report <- 100
formula <- ~ 1
# Note that this is just a test case and more iterations/chains may need to
# be run to ensure convergence.
out <- sfJSDM(formula = formula,
data = data.list,
inits = inits.list,
n.batch = n.batch,
batch.length = batch.length,
accept.rate = 0.43,
priors = prior.list,
cov.model = "matern",
tuning = tuning.list,
n.factors = 3,
n.omp.threads = 1,
verbose = TRUE,
NNGP = TRUE,
n.neighbors = 5,
search.type = 'cb',
n.report = 10,
n.burn = 0,
n.thin = 1,
n.chains = 2)
summary(out)
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