tMsPGOcc | R Documentation |
The function tMsPGOcc
fits multi-species multi-season occupancy models using Polya-Gamma data augmentation.
tMsPGOcc(occ.formula, det.formula, data, inits, priors, tuning,
n.batch, batch.length,
accept.rate = 0.43, n.omp.threads = 1,
verbose = TRUE, ar1 = FALSE, n.report = 100,
n.burn = round(.10 * n.batch * batch.length), n.thin = 1,
n.chains = 1, ...)
occ.formula |
a symbolic description of the model to be fit for the occurrence portion of the model using R's model syntax. Random intercepts are allowed using lme4 syntax (Bates et al. 2015). Only right-hand side of formula is specified. See example below. |
det.formula |
a symbolic description of the model to be fit for the detection portion of 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). |
data |
a list containing data necessary for model fitting.
Valid tags are |
inits |
a list with each tag corresponding to a parameter name.
Valid tags are |
priors |
a list with each tag corresponding to a parameter name.
Valid tags are |
tuning |
a list with each tag corresponding to a parameter
name. Valid tags are |
n.batch |
the number of MCMC batches in each chain to run for the Adaptive MCMC sampler. See Roberts and Rosenthal (2009) for details. |
batch.length |
the length of each MCMC batch to run for the Adaptive MCMC sampler. See Roberts and Rosenthal (2009) for details. |
accept.rate |
target acceptance rate for Adaptive MCMC. Defaul is 0.43. See Roberts and Rosenthal (2009) for details. |
n.omp.threads |
a positive integer indicating
the number of threads to use for SMP parallel processing within chains. This will have no
impact on model run times for non-spatial models. The package must
be compiled for OpenMP support. For most Intel-based machines, we
recommend setting |
verbose |
if |
ar1 |
logical value indicating whether to include an AR(1) zero-mean
temporal random effect in the model for each species. If |
n.report |
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. |
n.burn |
the number of samples out of the total |
n.thin |
the thinning interval for collection of MCMC samples. The
thinning occurs after the |
n.chains |
the number of chains to run in sequence. |
... |
currently no additional arguments |
An object of class tMsPGOcc
that is a list comprised of:
beta.comm.samples |
a |
alpha.comm.samples |
a |
tau.sq.beta.samples |
a |
tau.sq.alpha.samples |
a |
beta.samples |
a |
alpha.samples |
a |
theta.samples |
a |
eta.samples |
a three-dimensional array of posterior samples for the species-specific AR(1) random effects for each primary time period. Dimensions correspond to MCMC sample, species, and primary time period. |
z.samples |
a four-dimensional array of posterior samples for the latent occurrence values for each species. Dimensions corresopnd to MCMC sample, species, site, and primary time period. |
psi.samples |
a four-dimensional array of posterior samples for the latent occupancy probability values for each species. Dimensions correspond to MCMC sample, species, site, and primary time period. |
sigma.sq.psi.samples |
a |
sigma.sq.p.samples |
a |
beta.star.samples |
a |
alpha.star.samples |
a |
like.samples |
a four-dimensional array of posterior samples for the likelihood value used for calculating WAIC. Dimensions correspond to MCMC sample, species, site, and time period. |
rhat |
a list of Gelman-Rubin diagnostic values for some of the model parameters. |
ESS |
a list of effective sample sizes for some of the model parameters. |
run.time |
MCMC sampler execution time reported using |
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()
.
Some of the underlying code used for generating random numbers from the Polya-Gamma distribution is taken from the pgdraw package written by Daniel F. Schmidt and Enes Makalic. Their code implements Algorithm 6 in PhD thesis of Jesse Bennett Windle (2013) https://repositories.lib.utexas.edu/handle/2152/21842.
Jeffrey W. Doser doserjef@msu.edu,
Andrew O. Finley finleya@msu.edu
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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v067.i01")}.
Kery, M., & Royle, J. A. (2021). Applied hierarchical modeling in ecology: Analysis of distribution, abundance and species richness in R and BUGS: Volume 2: Dynamic and advanced models. Academic Press. Section 4.6.
# Simulate Data -----------------------------------------------------------
set.seed(500)
J.x <- 8
J.y <- 8
J <- J.x * J.y
# Years sampled
n.time <- sample(3:10, J, replace = TRUE)
# n.time <- rep(10, J)
n.time.max <- max(n.time)
# Replicates
n.rep <- matrix(NA, J, max(n.time))
for (j in 1:J) {
n.rep[j, 1:n.time[j]] <- sample(2:4, n.time[j], replace = TRUE)
}
N <- 7
# Community-level covariate effects
# Occurrence
beta.mean <- c(-3, -0.2, 0.5)
trend <- FALSE
sp.only <- 0
p.occ <- length(beta.mean)
tau.sq.beta <- c(0.6, 1.5, 1.4)
# Detection
alpha.mean <- c(0, 1.2, -1.5)
tau.sq.alpha <- c(1, 0.5, 2.3)
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]))
}
sp <- FALSE
dat <- simTMsOcc(J.x = J.x, J.y = J.y, n.time = n.time, n.rep = n.rep, N = N,
beta = beta, alpha = alpha, sp.only = sp.only, trend = trend,
psi.RE = psi.RE, p.RE = p.RE, sp = sp)
y <- dat$y
X <- dat$X
X.p <- dat$X.p
X.re <- dat$X.re
X.p.re <- dat$X.p.re
occ.covs <- list(occ.cov.1 = X[, , 2],
occ.cov.2 = X[, , 3])
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)
# 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))
z.init <- apply(y, c(1, 2, 3), function(a) as.numeric(sum(a, na.rm = TRUE) > 0))
inits.list <- list(alpha.comm = 0, beta.comm = 0, beta = 0,
alpha = 0, tau.sq.beta = 1, tau.sq.alpha = 1,
z = z.init)
# Tuning
tuning.list <- list(phi = 1)
# Number of batches
n.batch <- 5
# Batch length
batch.length <- 25
n.burn <- 25
n.thin <- 1
n.samples <- n.batch * batch.length
# Note that this is just a test case and more iterations/chains may need to
# be run to ensure convergence.
out <- tMsPGOcc(occ.formula = ~ occ.cov.1 + occ.cov.2,
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,
priors = prior.list,
n.omp.threads = 1,
verbose = TRUE,
n.report = 1,
n.burn = n.burn,
n.thin = n.thin,
n.chains = 1)
summary(out)
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