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# Single season occupancy with site covariates (not survey covariates)
# 'model' argument added 2013-12-02
# 'link' argument added 2015-02-20
occSScovSite <- function(y, n, model=NULL, data=NULL,
ci=0.95, link=c("logit", "probit"), ...) {
# single-season occupancy models with site-specific covatiates
# new version with y/n input; much faster!
# y is a vector with the number of detections at each site.
# n is a vector with the number of occasions at each site.
# model is a list of 2-sided formulae for psi and p; can also be a single
# 2-sided formula, eg, model = psi ~ habitat.
# ci is the required confidence interval.
if(length(n) == 1)
n <- rep(n, length(y))
if(length(y) != length(n))
stop("y and n must have the same length")
if(any(y > n))
stop("y cannot be greater than n")
crit <- fixCI(ci)
if(match.arg(link) == "logit") {
plink <- plogis
} else {
plink <- pnorm
}
# Standardise the model:
model <- stdModel(model, list(psi=~1, p=~1))
# Convert the covariate data frame into a list
nSites <- length(y)
dataList <- stddata(data, nocc=NULL)
psiDf <- selectCovars(model$psi, dataList, nSites)
if (nrow(psiDf) != nSites)
stop("Number of site covars doesn't match sites.")
psiModMat <- modelMatrix(model$psi, psiDf)
psiK <- ncol(psiModMat)
pDf <- selectCovars(model$p, dataList, nSites)
if (nrow(pDf) != nSites)
stop("Number of site covars doesn't match sites.")
pModMat <- modelMatrix(model$p, pDf)
pK <- ncol(pModMat)
K <- psiK + pK
# modelMatrix removes rows with NAs:
if(nrow(psiModMat) != nSites || nrow(pModMat) != nSites)
stop("Missing site covariates are not allowed.")
beta.mat <- matrix(NA_real_, K, 4)
colnames(beta.mat) <- c("est", "SE", "lowCI", "uppCI")
rownames(beta.mat) <- c(
paste("psi:", colnames(psiModMat)),
paste("p:", colnames(pModMat)))
lp.mat <- matrix(NA_real_, nSites*2, 3)
colnames(lp.mat) <- c("est", "lowCI", "uppCI")
rownames(lp.mat) <- c(
paste("psi:", 1:nSites, sep=""),
paste("p:", 1:nSites, sep=""))
logLik <- NA_real_
npar <- NA_integer_
varcov <- NULL
nll <- function(param){
psiBeta <- param[1:psiK]
pBeta <- param[(psiK+1):K]
logitpsi <- as.vector(psiModMat %*% psiBeta)
logpsi <- plink(logitpsi, log.p=TRUE)
log1mpsi <- plink( -logitpsi, log.p=TRUE)
logitp <- as.vector(pModMat %*% pBeta)
logp <- plink(logitp, log.p=TRUE)
log1mp <- plink( -logitp, log.p=TRUE)
logprob <- logAddExp(logpsi + logp * y + log1mp * (n - y),
log1mpsi + log(y==0))
return(min(-sum(logprob), .Machine$double.xmax))
}
# Run mle estimation with nlm:
# res <- nlm(nll, param, hessian=TRUE)
nlmArgs <- list(...)
nlmArgs$f <- nll
nlmArgs$p <- rep(0, K)
nlmArgs$hessian <- TRUE
res <- do.call(nlm, nlmArgs)
if(res$code > 2) # exit code 1 or 2 is ok.
warning(paste("Convergence may not have been reached (nlm code", res$code, ")"))
# Process output
beta.mat[,1] <- res$estimate
lp.mat[, 1] <- c(psiModMat %*% beta.mat[1:psiK, 1],
pModMat %*% beta.mat[(psiK+1):K, 1])
logLik <- -res$minimum
varcov0 <- try(chol2inv(chol(res$hessian)), silent=TRUE)
if (!inherits(varcov0, "try-error")) {
npar <- K
varcov <- varcov0
SE <- suppressWarnings(sqrt(diag(varcov)))
beta.mat[, 2] <- SE
beta.mat[, 3:4] <- sweep(outer(SE, crit), 1, res$estimate, "+")
temp <- c(getFittedVar(psiModMat, varcov[1:psiK, 1:psiK]),
getFittedVar(pModMat, varcov[(psiK+1):K, (psiK+1):K]))
if(all(temp >= 0)) {
SElp <- sqrt(temp)
lp.mat[, 2:3] <- sweep(outer(SElp, crit), 1, lp.mat[, 1], "+")
}
}
out <- list(call = match.call(),
link = match.arg(link),
beta = beta.mat,
beta.vcv = varcov,
real = plink(lp.mat),
logLik = c(logLik=logLik, df=npar, nobs=length(y)))
class(out) <- c("wiqid", "list")
return(out)
}
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