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#' Fit the N-mixture point count model
pcount <- function(formula, data, K, mixture = c("P", "NB", "ZIP"), starts,
method = "BFGS", se = TRUE,
engine = c("C", "R", "TMB"), threads = 1, ...)
{
# Check argument validity--------------------------------------------------
mixture <- match.arg(mixture, c("P", "NB", "ZIP"))
mixture_code <- switch(mixture, P = {1}, NB = {2}, ZIP = {3})
if(!is(data, "unmarkedFramePCount"))
stop("Data is not an unmarkedFramePCount object.")
engine <- match.arg(engine, c("C", "R", "TMB"))
if(any(sapply(split_formula(formula), has_random))) engine <- "TMB"
if(identical(mixture, "ZIP") & engine == "R")
stop("ZIP mixture not available for R engine")
# Generate design matrices-------------------------------------------------
designMats <- getDesign(data, formula)
X <- designMats$X; V <- designMats$V; y <- designMats$y
X.offset <- designMats$X.offset; V.offset <- designMats$V.offset
Z_state <- designMats$Z_state; Z_det <- designMats$Z_det
# Set up parameter names and indices---------------------------------------
lamParms <- colnames(X)
detParms <- colnames(V)
nDP <- ncol(V)
nAP <- ncol(X)
lamIdx <- 1:nAP
pIdx <- (nAP+1):(nAP+nDP)
n_param <- c(nAP, nDP, ifelse(mixture != "P", 1, 0))
nP <- sum(n_param)
nbParm <- switch(mixture, NB = "alpha", ZIP = "psi", P = character(0))
# Handle K (number of possible abundance values to marginalize over)-------
if(missing(K)) {
K <- max(y, na.rm = TRUE) + 100
warning("K was not specified and was set to ", K, ".")
}
if(K <= max(y, na.rm = TRUE))
stop("specified K is too small. Try a value larger than any observation")
#Minimum observed abundance at each site: Used by C++ and TMB
Kmin <- apply(y, 1, function(x) max(x, na.rm=TRUE))
# Specify negative log likelihood functions--------------------------------
if(identical(engine, "R")) {
k <- 0:K
M <- nrow(y)
J <- ncol(y)
k.ik <- rep(k, M)
k.ijk <- rep(k, M*J)
y.ij <- as.numeric(t(y))
y.ijk <- rep(y.ij, each = K + 1)
navec <- is.na(y.ijk)
ijk <- expand.grid(k = 0:K, j = 1:J, i = 1:M)
ijk.to.ikj <- with(ijk, order(i, k, j))
nll <- function(parms) {
theta.i <- exp(X %*% parms[lamIdx] + X.offset)
p.ij <- plogis(V %*% parms[pIdx] + V.offset)
theta.ik <- rep(theta.i, each = K + 1)
p.ijk <- rep(p.ij, each = K + 1)
bin.ijk <- dbinom(y.ijk,k.ijk,p.ijk)
bin.ijk[which(is.na(bin.ijk))] <- 1
bin.ik.mat <- matrix(bin.ijk[ijk.to.ikj], M * (K + 1), J,
byrow = TRUE)
g.ik <- rowProds(bin.ik.mat)
if(identical(mixture,"P")) {
f.ik <- dpois(k.ik,theta.ik)
}
else if (identical(mixture,"NB")){
f.ik <- dnbinom(k.ik, mu = theta.ik, size = exp(parms[nP]))
}
dens.i.mat <- matrix(f.ik * g.ik, M, K + 1, byrow = TRUE)
dens.i <- rowSums(dens.i.mat) # sum over the K
-sum(log(dens.i))
}
} else if(identical(engine, "C")) {
nll <- function(parms) {
nll_pcount(parms, n_param, y, X, V, X.offset, V.offset, K, Kmin,
mixture_code, threads)
}
}
# Fit model in C or R------------------------------------------------------
if(engine %in% c("C","R")){
if(missing(starts)) starts <- rep(0, nP)
if(length(starts) != nP)
stop(paste("The number of starting values should be", nP))
fm <- optim(starts, nll, method=method, hessian=se, ...)
ests <- fm$par
names(ests) <- c(lamParms, detParms, nbParm)
covMat <- invertHessian(fm, nP, se)
fmAIC <- 2 * fm$value + 2 * nP
tmb_mod <- NULL
# Organize fixed-effect estimates
state_coef <- list(ests=ests[lamIdx], cov=as.matrix(covMat[lamIdx,lamIdx]))
det_coef <- list(ests=ests[pIdx], cov=as.matrix(covMat[pIdx, pIdx]))
if(mixture %in% c("NB", "ZIP")){
scale_coef <- list(ests=ests[nP], cov=as.matrix(covMat[nP,nP]))
}
# No random effects in C or R engines
state_rand_info <- det_rand_info <- list()
# Fit model in TMB---------------------------------------------------------
} else if(engine == "TMB"){
# Set up TMB input data
forms <- split_formula(formula)
obs_all <- add_covariates(obsCovs(data), siteCovs(data), length(getY(data)))
inps <- get_ranef_inputs(forms, list(det=obs_all, state=siteCovs(data)),
list(V, X), designMats[c("Z_det","Z_state")])
tmb_dat <- c(list(y=y, K=K, Kmin=Kmin, mixture=mixture_code,
offset_state=X.offset, offset_det=V.offset), inps$data)
tmb_param <- c(inps$pars, list(beta_scale=rep(0,0)))
if(mixture_code > 1) tmb_param$beta_scale <- rep(0,1)
# Fit model in TMB
if(missing(starts)) starts <- NULL
tmb_out <- fit_TMB("tmb_pcount", tmb_dat, tmb_param, inps$rand_ef,
starts=starts, method, ...)
tmb_mod <- tmb_out$TMB
fm <- tmb_out$opt
fmAIC <- tmb_out$AIC
nll <- tmb_mod$fn
# Organize fixed-effect estimate from TMB output
state_coef <- get_coef_info(tmb_out$sdr, "state", lamParms, lamIdx)
det_coef <- get_coef_info(tmb_out$sdr, "det", detParms, pIdx)
if(mixture_code > 1){
scale_coef <- get_coef_info(tmb_out$sdr, "scale", nbParm, nP)
}
# Organize random-effect estimates from TMB output
state_rand_info <- get_randvar_info(tmb_out$sdr, "state", forms[[2]], siteCovs(data))
det_rand_info <- get_randvar_info(tmb_out$sdr, "det", forms[[1]], obs_all)
}
# Create unmarkedEstimates-------------------------------------------------
stateEstimates <- unmarkedEstimate(
name="Abundance", short.name="lam",
estimates = state_coef$ests, covMat = state_coef$cov, fixed=1:nAP,
invlink = "exp", invlinkGrad = "exp",
randomVarInfo=state_rand_info)
detEstimates <- unmarkedEstimate(
name = "Detection", short.name = "p",
estimates = det_coef$ests, covMat = det_coef$cov, fixed=1:nDP,
invlink = "logistic", invlinkGrad = "logistic.grad",
randomVarInfo=det_rand_info)
estimateList <- unmarkedEstimateList(list(state=stateEstimates,
det=detEstimates))
if(identical(mixture,"NB")) {
estimateList@estimates$alpha <- unmarkedEstimate(
name="Dispersion", short.name = "alpha",
estimates = scale_coef$ests, covMat = scale_coef$cov, fixed=1,
invlink = "exp", invlinkGrad = "exp", randomVarInfo=list())
}
if(identical(mixture,"ZIP")) {
estimateList@estimates$psi <- unmarkedEstimate(
name="Zero-inflation", short.name = "psi",
estimates = scale_coef$ests, covMat = scale_coef$cov, fixed=1,
invlink = "logistic", invlinkGrad = "logistic.grad", randomVarInfo=list())
}
# Create unmarkedFit object------------------------------------------------
umfit <- new("unmarkedFitPCount", fitType="pcount", call=match.call(),
formula = formula, data = data,
sitesRemoved = designMats$removed.sites,
estimates = estimateList, AIC = fmAIC, opt = fm,
negLogLike = fm$value,
nllFun = nll, K = K, mixture = mixture, TMB=tmb_mod)
return(umfit)
}
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