## Take an M x J matrix of detection probabilities and return a matrix
## of M x J observation probs
# Compute the cell probabilities for the observation classes
# in removal sampling.
#
# Both p and the returned matrix are M x J for M sites and J sampling occasions.
removalPiFun <- function(p){
M <- nrow(p)
J <- ncol(p)
pi <- matrix(NA, M, J)
pi[,1] <- p[,1]
for(i in seq(from = 2, length = J - 1)) {
pi[, i] <- pi[,i-1] / p[,i-1] * (1-p[,i-1]) * p[,i]
}
return(pi)
}
# p is an M x 2 matrix of detection probabilities (site x observer).
# returns an M x 3 matrix of row=(1 not 2, 2 not 1, 1 and 2).
# Compute the cell probabilities for the observation classes
# in double observer sampling.
doublePiFun <- function(p){
M <- nrow(p)
pi <- matrix(NA, M, 3)
pi[,1] <- p[,1] * (1 - p[,2])
pi[,2] <- p[,2] * (1 - p[,1])
pi[,3] <- p[,1] * p[,2]
return(pi)
}
# Fit the multinomial-Poisson abundance mixture model.
multinomPois <- function(formula, data, starts, method = "BFGS",
control = list(), se = TRUE)
{
if(!is(data, "unmarkedFrameMPois"))
stop("Data is not a data frame or unmarkedFrame.")
designMats <- getDesign(data, formula)
X <- designMats$X; V <- designMats$V; y <- designMats$y
X.offset <- designMats$X.offset; V.offset <- designMats$V.offset
if (is.null(X.offset)) {
X.offset <- rep(0, nrow(X))
}
if (is.null(V.offset)) {
V.offset <- rep(0, nrow(V))
}
J <- ncol(y)
R <- obsNum(data)
M <- nrow(y)
piFun <- data@piFun
lamParms <- colnames(X)
detParms <- colnames(V)
nDP <- ncol(V)
nAP <- ncol(X)
nP <- nDP + nAP
if(!missing(starts) && length(starts) != nP)
stop(paste("The number of starting values should be", nP))
yvec <- as.numeric(y)
navec <- is.na(yvec)
nll <- function(parms) {
lambda <- exp(X %*% parms[1 : nAP] + X.offset)
p <- plogis(V %*% parms[(nAP + 1) : nP] + V.offset)
p.matrix <- matrix(p, M, R, byrow = TRUE)
pi <- do.call(piFun, list(p = p.matrix))
logLikeSite <- dpois(y, matrix(lambda, M, J) * pi, log = TRUE)
logLikeSite[navec] <- 0
-sum(logLikeSite)
}
if(missing(starts))
starts <- rep(0, nP)
fm <- optim(starts, nll, method = method, hessian = se, control = control)
opt <- fm
if(se) {
tryCatch(covMat <- solve(fm$hessian),
error=function(x) stop(simpleError("Hessian is singular. Try using fewer covariates.")))
} else {
covMat <- matrix(NA, nP, nP)
}
ests <- fm$par
fmAIC <- 2 * fm$value + 2 * nP
names(ests) <- c(lamParms, detParms)
stateName <- "Abundance"
stateEstimates <- unmarkedEstimate(name = stateName, short.name = "lambda",
estimates = ests[1:nAP],
covMat = as.matrix(covMat[1:nAP,1:nAP]), invlink = "exp",
invlinkGrad = "exp")
detEstimates <- unmarkedEstimate(name = "Detection", short.name = "p",
estimates = ests[(nAP + 1) : nP],
covMat = as.matrix(covMat[(nAP + 1) : nP, (nAP + 1) : nP]),
invlink = "logistic", invlinkGrad = "logistic.grad")
estimateList <- unmarkedEstimateList(list(state=stateEstimates,
det=detEstimates))
umfit <- new("unmarkedFitMPois", fitType = "multinomPois",
call = match.call(), formula = formula, data = data,
estimates = estimateList, sitesRemoved = designMats$removed.sites,
AIC = fmAIC, opt = opt, negLogLike = fm$value, nllFun = nll)
return(umfit)
}