# Royel et al. 2004 distance sampling
distsamp <- function(formula, data,
keyfun=c("halfnorm", "exp", "hazard", "uniform"),
output=c("density", "abund"), unitsOut=c("ha", "kmsq"), starts=NULL,
method="BFGS", control=list(), se = TRUE)
{
keyfun <- match.arg(keyfun)
output <- match.arg(output)
unitsOut <- match.arg(unitsOut)
db <- data@dist.breaks
tdWsq <- 2 / max(db)^2 # only used for pt-transects
strip.widths <- diff(db) # only used for line-transects
tlength <- data@tlength
survey <- data@survey
unitsIn <- data@unitsIn
designMats <- getDesign(data, formula)
X <- designMats$X; V <- designMats$V; y <- designMats$y
X.offset <- designMats$X.offset; V.offset <- designMats$V.offset
if (is.null(X.offset)) {
X.offset <- rep(0, nrow(X))
}
if (is.null(V.offset)) {
V.offset <- rep(0, nrow(V))
}
a <- calcAreas(dist.breaks = db, tlength = tlength,
survey = survey, output = output, M = numSites(data),
J = ncol(getY(data)), unitsIn = unitsIn, unitsOut = unitsOut)
if(length(designMats$removed.sites)>0)
a <- a[-designMats$removed.sites,]
M <- nrow(y)
J <- ncol(y)
namat <- is.na(y)
lamParms <- colnames(X)
detParms <- colnames(V)
nAP <- length(lamParms)
nDP <- length(detParms)
nP <- nAP + nDP
pi <- matrix(NA, M, J)
switch(keyfun,
halfnorm = {
altdetParms <- paste("sigma", colnames(V), sep="")
if(is.null(starts)) {
starts <- c(rep(0, nAP), log(max(db)), rep(0, nDP-1))
names(starts) <- c(lamParms, detParms)
} else {
if(is.null(names(starts))) names(starts) <- c(lamParms, detParms)
}
nll <- function(param) {
sigma <- drop(exp(V %*% param[(nAP+1):nP] + V.offset))
lambda <- drop(exp(X %*% param[1:nAP] + X.offset))
for(i in 1:M)
{
switch(survey,
line = {
f.0 <- 2 * dnorm(0, 0, sd=sigma[i])
int <- 2 * (pnorm(db[-1], 0, sd=sigma[i]) -
pnorm(db[-(J+1)], 0, sd=sigma[i]))
pi[i,] <- int / f.0 / strip.widths
},
point = {
for(j in 1:J) {
pi[i, j] <- tdWsq * integrate(grhn, db[j], db[j+1],
sigma = sigma[i])$value
}
})
}
ll <- dpois(y, lambda * pi * a, log=TRUE)
ll[namat] <- 0
-sum(ll)
}},
exp = {
altdetParms <- paste("rate", colnames(V), sep="")
if(is.null(starts)) {
starts <- c(rep(0, nAP), 0, rep(0, nDP-1))
names(starts) <- c(lamParms, detParms)
} else {
if(is.null(names(starts)))
names(starts) <- c(lamParms, detParms)
}
nll <- function(param) {
rate <- drop(exp(V %*% param[(nAP+1):nP] + V.offset))
lambda <- drop(exp(X %*% param[1:nAP] + X.offset))
for(i in 1:M)
{
switch(survey,
line = {
for(j in 1:J) {
pi[i, j] <- integrate(gxexp, db[j], db[j+1],
rate=rate[i])$value / strip.widths[j]
}
},
point = {
for(j in 1:J) {
pi[i, j] <- tdWsq * integrate(grexp, db[j], db[j+1],
rate = rate[i])$value
}
})
}
ll <- dpois(y, lambda * pi * a, log=TRUE)
ll[namat] <- 0
-sum(ll)
}},
hazard = {
nDP <- length(detParms)
nP <- nAP + nDP + 1
altdetParms <- paste("shape", colnames(V), sep="")
if(is.null(starts)) {
starts <- c(rep(0, nAP), log(median(db)), rep(0, nDP-1), 1)
names(starts) <- c(lamParms, detParms, "scale")
} else {
if(is.null(names(starts)))
names(starts) <- c(lamParms, detParms, "scale")
}
nll <- function(param) {
shape <- drop(exp(V %*% param[(nAP+1):(nP-1)] + V.offset))
scale <- drop(exp(param[nP]))
lambda <- drop(exp(X %*% param[1:nAP] + X.offset))
for(i in 1:M)
{
switch(survey,
line = {
for(j in 1:J) {
pi[i, j] <- integrate(gxhaz, db[j], db[j+1],
shape=shape[i], scale=scale)$value / strip.widths[j]
}
},
point = {
for(j in 1:J) {
pi[i, j] <- tdWsq * integrate(grhaz, db[j], db[j+1],
shape = shape[i], scale=scale)$value
}
})
}
ll <- dpois(y, lambda * pi * a, log=TRUE)
ll[namat] <- 0
-sum(ll)
}},
uniform = {
detParms <- character(0)
altdetParms <- character(0)
nDP <- 0
if(is.null(starts)) {
starts <- rep(0, length(lamParms))
names(starts) <- lamParms
} else {
if(is.null(names(starts)))
names(starts) <- lamParms
}
nll <- function(param)
{
lambda <- drop(exp(X %*% param + X.offset))
ll <- dpois(y, lambda * a, log=TRUE)
ll[namat] <- 0
-sum(ll)
}
})
fm <- optim(starts, nll, method=method, hessian=se, control=control)
opt <- fm
ests <- fm$par
if(se) {
covMat <- tryCatch(solve(fm$hessian), error=function(x)
stop(simpleError("Hessian is singular. Try using fewer covariates or providing starting values.")))
if(class(covMat)[1] == "simpleError") {
print(covMat$message)
covMat <- matrix(NA, nP, nP)
}
} else {
covMat <- matrix(NA, nP, nP)
}
estsAP <- ests[1:nAP]
if(keyfun == "hazard") {
estsDP <- ests[(nAP+1):(nP-1)]
estsScale <- ests[nP]
}
else
estsDP <- ests[(nAP+1):nP]
covMatAP <- covMat[1:nAP, 1:nAP, drop=F]
if(keyfun=="hazard") {
covMatDP <- covMat[(nAP+1):(nP-1), (nAP+1):(nP-1), drop=F]
covMatScale <- covMat[nP, nP, drop=F]
}
else if(keyfun!="uniform")
covMatDP <- covMat[(nAP+1):nP, (nAP+1):nP, drop=F]
names(estsDP) <- altdetParms
fmAIC <- 2 * fm$value + 2 * nP
stateName <- switch(output, abund = "Abundance", density = "Density")
stateEstimates <- unmarkedEstimate(name = stateName,
short.name = "lam", estimates = estsAP, covMat = covMatAP,
invlink = "exp", invlinkGrad = "exp")
if (keyfun != "uniform") {
detEstimates <- unmarkedEstimate(name = "Detection", short.name = "p",
estimates = estsDP, covMat = covMatDP, invlink = "exp",
invlinkGrad = "exp")
if(keyfun != "hazard")
estimateList <- unmarkedEstimateList(list(state=stateEstimates,
det=detEstimates))
else {
scaleEstimates <- unmarkedEstimate(name = "Hazard-rate(scale)",
short.name = "p", estimates = estsScale,
covMat = covMatScale, invlink = "exp", invlinkGrad = "exp")
estimateList <- unmarkedEstimateList(list(state=stateEstimates,
det=detEstimates, scale=scaleEstimates))
}
} else {
estimateList <- unmarkedEstimateList(list(state=stateEstimates))
}
dsfit <- new("unmarkedFitDS", fitType = "distsamp", call = match.call(),
opt = opt, formula = formula, data = data, keyfun=keyfun,
sitesRemoved = designMats$removed.sites, unitsOut=unitsOut,
estimates = estimateList, AIC = fmAIC, negLogLike = fm$value,
nllFun = nll, output=output)
return(dsfit)
}
# Detection functions
gxhn <- function(x, sigma) exp(-x^2/(2 * sigma^2))
gxexp <- function(x, rate) exp(-x / rate)
gxhaz <- function(x, shape, scale) 1 - exp(-(x/shape)^-scale)
grhn <- function(r, sigma) exp(-r^2/(2 * sigma^2)) * r
grexp <- function(r, rate) exp(-r / rate) * r
grhaz <- function(r, shape, scale) (1 - exp(-(r/shape)^-scale)) * r
dxhn <- function(x, sigma)
gxhn(x=x, sigma=sigma) / integrate(gxhn, 0, Inf, sigma=sigma)$value
drhn <- function(r, sigma)
grhn(r=r, sigma=sigma) / integrate(grhn, 0, Inf, sigma=sigma)$value
dxexp <- function(x, rate)
gxexp(x=x, rate=rate) / integrate(gxexp, 0, Inf, rate=rate)$value
drexp <- function(r, rate)
grexp(r=r, rate=rate) / integrate(grexp, 0, Inf, rate=rate)$value
dxhaz <- function(x, shape, scale)
gxhaz(x=x, shape=shape, scale=scale) / integrate(gxhaz, 0, Inf,
shape=shape, scale=scale)$value
drhaz <- function(r, shape, scale)
grhaz(r=r, shape=shape, scale=scale) / integrate(grhaz, 0, Inf,
shape=shape, scale=scale)$value
# Vectorized version of integrate()
vIntegrate <- Vectorize(integrate, c("lower", "upper"))
# Multinomial cell probabilities for line or point transects under half-normal model. These are still used by getP but not distsamp.
cp.hn <- function(d, s, survey)
{
switch(survey,
line = {
strip.widths <- diff(d)
f.0 <- 2 * dnorm(0, 0, sd=s)
int <- 2 * (pnorm(d[-1], 0, sd=s) - pnorm(d[-length(d)], 0, sd=s))
cp <- int / f.0 / strip.widths
},
point = {
W <- max(d)
int <- as.numeric(vIntegrate(grhn, d[-length(d)], d[-1],
sigma=s)["value",])
cp <- 2 / W^2 * int
})
return(cp)
}
cp.exp <- function(d, rate, survey)
{
switch(survey,
line = {
strip.widths <- diff(d)
# f.0 <- dexp(0, rate=rate)
# int <- pexp(d[-1], rate=rate) - pexp(d[-length(d)], rate=rate)
int <- as.numeric(vIntegrate(gxexp, d[-length(d)], d[-1],
rate=rate)["value",])
cp <- int / strip.widths
},
point = {
W <- max(d)
int <- as.numeric(vIntegrate(grexp, d[-length(d)], d[-1],
rate=rate)["value",])
cp <- 2 / W^2 * int
})
return(cp)
}
cp.haz <- function(d, shape, scale, survey)
{
switch(survey,
line = {
strip.widths <- diff(d)
int <- as.numeric(vIntegrate(gxhaz, d[-length(d)], d[-1],
shape=shape, scale=scale)["value",])
cp <- int / strip.widths
},
point = {
W <- max(d)
int <- as.numeric(vIntegrate(grhaz, d[-length(d)], d[-1],
shape=shape, scale=scale)["value",])
cp <- 2 / W^2 * int
})
return(cp)
}
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