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# Fit the time-to-detection model of Garrard et al. 2008, 2013
# with dynamic extension
occuTTD <- function(psiformula=~1, gammaformula=~1, epsilonformula=~1,
detformula=~1, data, ttdDist=c('exp','weibull'),
linkPsi = c("logit", "cloglog"), starts, method = "BFGS",
se = TRUE, engine = c("C", "R"), ...) {
#Check arguments-------------------------------------------------------------
if(!is(data, "unmarkedFrameOccuTTD")){
stop("Data is not an unmarkedFrameOccuTTD object.")
}
engine <- match.arg(engine, c("C", "R"))
ttdDist <- match.arg(ttdDist, c("exp","weibull"))
linkPsi <- match.arg(linkPsi, c("logit","cloglog"))
formula <- list(psiformula, gammaformula, epsilonformula, detformula)
check_no_support(formula)
formula <- as.formula(paste(unlist(formula),collapse=" "))
#Psi link function
linkFunc <- plogis
invlink <- "logistic"
linkGrad <- "logistic.grad"
if(linkPsi == "cloglog"){
linkFunc <- cloglog
invlink <- "cloglog"
linkGrad <- "cloglog.grad"
}
#Process input data----------------------------------------------------------
designMats <- getDesign(data, formula)
#V = detection; W = occupancy
V <- designMats$V; W <- designMats$W
X.gam <- designMats$X.gam; X.eps <- designMats$X.eps
y <- designMats$y
removed <- designMats$removed.sites
N <- nrow(y)
R <- ncol(y)
T <- data@numPrimary
J <- R / T
#Reformat data for likelihood
yvec <- as.numeric(t(y))
naflag <- as.numeric(is.na(yvec))
surveyLength <- data@surveyLength
if(length(removed>0)) surveyLength <- surveyLength[-removed,]
ymax <- as.numeric(t(surveyLength))
delta <- as.numeric(yvec<ymax)
#Organize parameters---------------------------------------------------------
detParms <- colnames(V); nDP <- ncol(V)
occParms <- colnames(W); nOP <- ncol(W)
psi_inds <- 1:nOP
gamParms <- NULL; nGP <- 0; col_inds <- c(0,0)
epsParms <- NULL; nEP <- 0; ext_inds <- c(0,0)
if(T>1){
#Remove final year from col/ext design matrices
X.gam <- as.matrix(X.gam[-seq(T,N*T,by=T),,drop=FALSE])
X.eps <- as.matrix(X.eps[-seq(T,N*T,by=T),,drop=FALSE])
gamParms <- colnames(X.gam); nGP <- ncol(X.gam)
epsParms <- colnames(X.eps); nEP <- ncol(X.eps)
col_inds <- (nOP+1):(nOP+nGP)
ext_inds <- (nOP+nGP+1):(nOP+nGP+nEP)
}
det_inds <- (nOP+nGP+nEP+1):(nOP+nGP+nEP+nDP)
parms <- c(occParms,gamParms,epsParms,detParms)
if(ttdDist == "weibull") parms <- c(parms, "k")
nP <- length(parms)
#Likelihood functions--------------------------------------------------------
nll_R <- function(params){
#Get occupancy and detection parameters
psi <- linkFunc(W %*% params[psi_inds])
psi <- cbind(1-psi, psi)
lam <- exp(V %*% params[det_inds])
#Simplified version of Garrard et al. 2013 eqn 5
#Extended to Weibull
if(ttdDist=='weibull'){
k <- exp(params[nP])
e_lamt <- ( k*lam*(lam*yvec)^(k-1) )^delta * exp(-1*(lam*yvec)^k)
} else {
e_lamt <- lam^delta * exp(-lam*yvec)
}
#Get probability of y for each z state
get_Py <- function(e_lamt, delta){
sum_delt <- as.numeric(sum(delta, na.rm=T)>0)
c(1-sum_delt, prod(e_lamt[!is.na(e_lamt)]))
}
#If dynamic, get col/ext probs and transition prob matrix
if(T>1){
col <- plogis(X.gam %*% params[col_inds])
ext <- plogis(X.eps %*% params[ext_inds])
phi <- cbind(1-col, col, ext, 1-ext)
}
#Begin likelihood calculation
lik <- rep(NA,N)
ystart <- 1
phi_index <- 1
for (n in 1:N){
phi_prod <- diag(2)
#If dynamic, iterate through primary periods
if(T>1){
for (t in 1:(T-1)){
yend <- ystart+J-1
D_pt <- diag(get_Py(e_lamt[ystart:yend], delta[ystart:yend]))
phi_t <- matrix(phi[phi_index,],nrow=2, byrow=TRUE)
phi_prod <- phi_prod %*% ( D_pt %*% phi_t )
ystart <- ystart + J
phi_index <- phi_index + 1
}
}
yend <- ystart+J-1
p_T <- get_Py(e_lamt[ystart:yend], delta[ystart:yend])
ystart <- ystart + J
lik[n] <- psi[n,] %*% phi_prod %*% p_T
}
-sum(log(lik))
}
nll_C <- function(params){
.Call("nll_occuTTD",
params, yvec, delta, W, V, X.gam, X.eps,
range(psi_inds)-1, range(det_inds)-1,
range(col_inds)-1, range(ext_inds)-1,
linkPsi, ttdDist, N, T, J, naflag,
PACKAGE = "unmarked")
}
nll <- nll_C
if(engine == "R") nll <- nll_R
#Run optim()-----------------------------------------------------------------
if(!missing(starts) && length(starts) != nP)
stop(paste("The number of starting values should be", nP))
if(missing(starts)) starts <- rep(0, nP)
fm <- optim(starts, nll, method = method, hessian = se, ...)
covMat <- invertHessian(fm, nP, se)
#Build output object---------------------------------------------------------
ests <- fm$par
fmAIC <- 2 * fm$value + 2 * nP #+ 2*nP*(nP + 1)/(M - nP - 1)
names(ests) <- parms
psi <- unmarkedEstimate(name = "Occupancy", short.name = "psi",
estimates = ests[psi_inds],
covMat = as.matrix(covMat[psi_inds,psi_inds]),
invlink = invlink,
invlinkGrad = linkGrad)
det <- unmarkedEstimate(name = "Detection", short.name = "lam",
estimates = ests[det_inds],
covMat = as.matrix(covMat[det_inds,det_inds]),
invlink = "exp",
invlinkGrad = "exp")
if(T>1){
col <- unmarkedEstimate(name = "Colonization", short.name = "col",
estimates = ests[col_inds],
covMat = as.matrix(covMat[col_inds,col_inds]),
invlink = "logistic",
invlinkGrad = "logistic.grad")
ext <- unmarkedEstimate(name = "Extinction", short.name = "ext",
estimates = ests[ext_inds],
covMat = as.matrix(covMat[ext_inds,ext_inds]),
invlink = "logistic",
invlinkGrad = "logistic.grad")
estimateList <- unmarkedEstimateList(list(psi = psi, col = col,
ext = ext, det=det))
} else {
estimateList <- unmarkedEstimateList(list(psi = psi, det=det))
}
#Add Weibull shape parameter if necessary
if(ttdDist=="weibull"){
estimateList@estimates$shape <- unmarkedEstimate(name = "Weibull shape",
short.name = "k", estimates = ests[nP],
covMat = as.matrix(covMat[nP, nP]), invlink = "exp",
invlinkGrad = "exp")
}
umfit <- new("unmarkedFitOccuTTD", fitType = "occuTTD",
call = match.call(),
formula = formula,
psiformula = psiformula,
gamformula = gammaformula,
epsformula = epsilonformula,
detformula = detformula,
data = data, sitesRemoved = removed,
estimates = estimateList,
AIC = fmAIC, opt = fm, negLogLike = fm$value,
nllFun = nll)
return(umfit)
}
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