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main-missing-sim.R
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main-missing-sim.R
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# main-missing-sim.R: script to perform the simulation study comparing the
# five candidate models in their ability to predict
# a species-environment relationship from the "Missing"
# scenario.
# Author: Jeffrey W. Doser
rm(list = ls())
library(spOccupancy)
# Functions ---------------------------------------------------------------
logit <- function(theta, a = 0, b = 1) {log((theta-a)/(b-theta))}
logit.inv <- function(z, a = 0, b = 1) {b-(b-a)/(1+exp(z))}
# Parameters for simulations ----------------------------------------------
# Number of data sets simulated for each scenario
n.sims <- 50
# Set seed to generate same values
set.seed(1111)
# Random seeds for each data set
my.seeds <- sample(1:100000, n.sims, replace = FALSE)
# Simulation scenarios
model.types <- c('linear', 'quadratic', 'stratum', 'interaction', 'svc')
# Total number of candidate models
n.models <- length(model.types)
# Number of spatial locations
J.x <- 20
J.y <- 20
J <- J.x * J.y
# Simulation setup --------------------------------------------------------
waic.vals <- array(NA, dim = c(n.sims, n.models))
beta.effect.true.vals <- array(NA, dim = c(n.sims, J))
beta.effect.mean.vals <- array(NA, dim = c(n.sims, J, n.models))
# MCMC Info ---------------------------
n.samples <- 15000
batch.length <- 25
n.batch <- n.samples / batch.length
n.burn <- 10000
n.thin <- 5
n.chains <- 1
accept.rate <- 0.43
# Set parameters and values -----------------------------------------------
# Matrix of spatial locations
s.x <- seq(0, 1, length.out = J.x)
s.y <- seq(0, 1, length.out = J.y)
coords <- as.matrix(expand.grid(s.x, s.y))
# Get strata for each cell
strata <- ifelse(coords[, 1] <= .33 & coords[, 2] <= .33, 1,
ifelse(coords[, 1] <= .33 & coords[, 2] <= .67, 2,
ifelse(coords[, 1] <= .33 & coords[, 2] <= 1, 3,
ifelse(coords[, 1] <= .67 & coords[, 2] <= .33, 4,
ifelse(coords[, 1] <= .67 & coords[, 2] <= .67, 5,
ifelse(coords[, 1] <= .67 & coords[, 2] <= 1, 6,
ifelse(coords[, 1] <= 1 & coords[, 2] <= .33, 7,
ifelse(coords[, 1] <= 1 & coords[, 2] <= .67, 8,
9))))))))
# Main covariate
x.1 <- seq(from = -5, to = 5, length.out = J)
x.interaction <- c(t(matrix(x.1, J.x, J.y)))
beta.0 <- 0
beta.linear <- 0
beta.quadratic <- -0.2
beta.strata <- runif(length(unique(strata)), -1, 1)
beta.interaction <- 0.4
beta.miss.int <- 0.5
sigma.sq <- 2
phi <- 3 / .8
Sigma <- spBayes::mkSpCov(coords, as.matrix(sigma.sq), as.matrix(0), as.matrix(phi), 'exponential')
x.miss.int <- MASS::mvrnorm(1, rep(0, J), Sigma)
# Do the simulations ------------------------------------------------------
for (j in 1:n.sims) {
print(paste("Currently on simulation set ", j, " out of ", n.sims, sep = ''))
set.seed(my.seeds[j])
# Simulate the data set -------------------------------------------------
logit <- function(theta, a = 0, b = 1){log((theta-a)/(b-theta))}
logit.inv <- function(z, a = 0, b = 1){b-(b-a)/(1+exp(z))}
# Form detection covariate (if any) -------------------------------------
# Assume constant detection
n.rep <- rep(3, J)
n.rep.max <- max(n.rep)
alpha <- c(0.5)
n.alpha <- length(alpha)
X.p <- array(NA, dim = c(J, n.rep.max, n.alpha))
# Get index of surveyed replicates for each site.
rep.indx <- list()
for (k in 1:J) {
rep.indx[[k]] <- sample(1:n.rep.max, n.rep[k], replace = FALSE)
}
X.p[, , 1] <- 1
if (n.alpha > 1) {
for (i in 2:n.alpha) {
for (k in 1:J) {
X.p[k, rep.indx[[k]], i] <- rnorm(n.rep[k])
} # j
} # i
}
# Latent Occupancy Process ----------------------------------------------
psi <- logit.inv(beta.0 + beta.linear * x.1 + beta.miss.int * x.miss.int * x.1)
z <- rbinom(J, 1, psi)
# Data Formation --------------------------------------------------------
p <- matrix(NA, nrow = J, ncol = n.rep.max)
y <- matrix(NA, nrow = J, ncol = n.rep.max)
for (k in 1:J) {
p[k, rep.indx[[k]]] <- logit.inv(X.p[k, rep.indx[[k]], ] %*% as.matrix(alpha))
y[k, rep.indx[[k]]] <- rbinom(n.rep[k], 1, p[k, rep.indx[[k]]] * z[k])
} # j
data.list <- list(y = y,
occ.covs = data.frame(x = x.1,
x.interaction = x.interaction,
strata = strata),
coords = coords)
beta.effect.true.vals[j, ] <- beta.linear + beta.miss.int * x.miss.int
for (i in 1:n.models) {
print(paste("Currently on model ", i, " out of ", n.models, sep = ''))
curr.model <- model.types[i]
phi.tune <- 0.5
# Priors
prior.list <- list(beta.normal = list(mean = 0, var = 2.72),
alpha.normal = list(mean = 0, var = 2.72),
sigma.sq.ig = list(a = 2, b = 1),
phi.unif = list(a = 3 / 1, b = 3 / 0.1))
# Starting values
z.init <- apply(y, 1, function(a) as.numeric(sum(a, na.rm = TRUE) > 0))
inits.list <- list(beta = 0, alpha = 0, sigma.sq = 1, phi = 3 / 0.5,
z = z.init)
# Tuning
tuning.list <- list(phi = phi.tune)
# Determine occupancy formula
if (curr.model == 'linear') {
occ.formula <- ~ x
} else if (curr.model == 'quadratic') {
occ.formula <- ~ x + I(x^2)
} else if (curr.model == 'stratum') {
occ.formula <- ~ x + x:factor(strata)
} else if (curr.model == 'interaction') {
occ.formula <- ~ x + x:x.interaction
} else if (curr.model == 'svc') {
occ.formula <- ~ x
}
if (curr.model != 'svc') {
out <- PGOcc(occ.formula = occ.formula,
det.formula = ~ 1,
data = data.list,
n.samples = n.batch * batch.length,
inits = inits.list,
priors = prior.list,
verbose = TRUE,
n.report = 1000,
n.burn = n.burn,
n.thin = n.thin,
n.chains = 1)
} else {
n.samples <- 30000
batch.length <- 25
n.batch <- n.samples / batch.length
n.burn <- 20000
n.thin <- 10
out <- svcPGOcc(occ.formula = occ.formula,
det.formula = ~ 1,
svc.cols = 2,
data = data.list,
n.batch = n.batch,
batch.length = batch.length,
inits = inits.list,
priors = prior.list,
accept.rate = 0.43,
cov.model = 'exponential',
tuning = tuning.list,
n.omp.threads = 2, # Change as desired.
verbose = TRUE,
NNGP = TRUE,
n.neighbors = 5,
n.report = 25,
n.burn = n.burn,
n.thin = n.thin,
n.chains = 1)
}
waic.vals[j, i] <- waicOcc(out)[3]
if (curr.model == 'linear') {
beta.effect.mean.vals[j, , i] <- mean(out$beta.samples[, 2])
}
if (curr.model == 'quadratic') {
beta.effect.mean.vals[j, , i] <- mean(out$beta.samples[, 2]) + mean(out$beta.samples[, 3]) * x.1
}
if (curr.model == 'stratum') {
beta.mean.vals <- apply(out$beta.samples[, -1], 2, mean)
beta.mean.vals[-1] <- beta.mean.vals[-1] + beta.mean.vals[1]
beta.effect.mean.vals[j, , i] <- beta.mean.vals[strata]
}
if (curr.model == 'interaction') {
beta.effect.mean.vals[j, , i] <- mean(out$beta.samples[, 2]) + mean(out$beta.samples[, 3]) * x.interaction
}
if (curr.model == 'svc') {
beta.effect.mean.vals[j, , i] <- apply(getSVCSamples(out)[[1]], 2, mean)
}
} # i (n.scenarios)
} # j (n.sims)
# Save results ------------------------------------------------------------
save(waic.vals, beta.effect.true.vals, beta.effect.mean.vals,
file = 'results/sim-true-missing.rda')