I have written a custom likelihood function that fits a multi-data model that integrates mark-recapture and telemetry data (sensu Royle et al. 2013 Methods in Ecology and Evolution). The likelihood function is designed to be flexible in terms of whether and how many covariates are specified for different linear models in different likelihood components which is determined by values supplied as function arguments (i.e., data matrices "detcovs" and "dencovs" in my code). The likelihood function works when I directly supply it to optimization functions (e.g., optim or nlm), but does not play nice with the mle2 function in the bbmle package. My problem is that I continually run into the following error: "some named arguments in 'start' are not arguments to the specified log-likelihood function". This is my first attempt at writing custom likelihood functions so I'm sure there are general coding conventions of which I'm unaware that make such tasks much more efficient and amendable to the mle2 function. Below is my likelihood function, code creating the staring value objects, and code calling the mle2 function. Any advice how to solve the error problem and general comments on writing cleaner functions is welcome. Many thanks in advance.
Edit: As requested, I have simplified the likelihood function and provided code to simulate reproducible data to which the model can be fit. Included in the simulation code are 2 custom functions and use of the raster function from the raster package. Hopefully, I have sufficiently simplified everything to enable others to troubleshoot. Again, many thanks for your help!
Jared
Likelihood function:
CSCR.RSF.intlik2.EXAMPLE <- function(alpha0,sigma,alphas=NULL,betas=NULL,n0,yscr=NULL,K=NULL,X=X,trapcovs=NULL,Gden=NULL,Gdet=NULL,ytel=NULL,stel=NULL,
dencovs=NULL,detcovs=NULL){
#
# this version of the code handles a covariate on log(Density). This is starting value 5
#
# start = vector of starting values
# yscr = nind x ntraps encounter matrix
# K = number of occasions
# X = trap locations
# Gden = matrix with grid cell coordinates for density raster
# Gdet = matrix with gride cell coordinates for RSF raster
# dencovs = all covariate values for all nGden pixels in density raster
# trapcovs = covariate value at trap locations
# detcovs = all covariate values for all nGrsf pixels in RSF raster
# ytel = nguys x nGdet matrix of telemetry fixes in each nGdet pixels
# stel = home range center of telemetered individuals, IF you wish to estimate it. Not necessary
# alphas = starting values for RSF/detfn coefficients excluding sigma and intercept
# alpha0 = starting values for RSF/detfn intercept
# sigma = starting value for RSF/detfn sigma
# betas = starting values for density function coefficients
# n0 = starting value for number of undetected individuals on log scale
#
n0 = exp(n0)
nGden = nrow(Gden)
D = e2dist(X,Gden)
nGdet <- nrow(Gdet)
alphas = alphas
loglam = alpha0 -(1/(2*sigma*sigma))*D*D + as.vector(trapcovs%*%alphas) # ztrap recycled over nG
psi = exp(as.vector(dencovs%*%betas))
psi = psi/sum(psi)
probcap = 1-exp(-exp(loglam))
#probcap = (exp(theta0)/(1+exp(theta0)))*exp(-theta1*D*D)
Pm = matrix(NA,nrow=nrow(probcap),ncol=ncol(probcap))
ymat = yscr
ymat = rbind(yscr,rep(0,ncol(yscr)))
lik.marg = rep(NA,nrow(ymat))
for(i in 1:nrow(ymat)){
Pm[1:length(Pm)] = (dbinom(rep(ymat[i,],nGden),rep(K,nGden),probcap[1:length(Pm)],log=TRUE))
lik.cond = exp(colSums(Pm))
lik.marg[i] = sum( lik.cond*psi )
}
nv = c(rep(1,length(lik.marg)-1),n0)
part1 = lgamma(nrow(yscr)+n0+1) - lgamma(n0+1)
part2 = sum(nv*log(lik.marg))
out = -1*(part1+ part2)
lam = t(exp(a0 - (1/(2*sigma*sigma))*t(D2)+ as.vector(detcovs%*%alphas)))# recycle zall over all ytel guys
# lam is now nGdet x nG!
denom = rowSums(lam)
probs = lam/denom # each column is the probs for a guy at column [j]
tel.loglik = -1*sum( ytel*log(probs) )
out = out + tel.loglik
out
}
Data simulation code:
library(raster)
library(bbmle)
e2dist <- function (x, y){
i <- sort(rep(1:nrow(y), nrow(x)))
dvec <- sqrt((x[, 1] - y[i, 1])^2 + (x[, 2] - y[i, 2])^2)
matrix(dvec, nrow = nrow(x), ncol = nrow(y), byrow = F)
}
spcov <- function(R) {
v <- sqrt(nrow(R))
D <- as.matrix(dist(R))
V <- exp(-D/2)
cov1 <- t(chol(V)) %*% rnorm(nrow(R))
Rd <- as.data.frame(R)
colnames(Rd) <- c("x", "y")
Rd$C <- as.numeric((cov1 - mean(cov1)) / sd(cov1))
return(Rd)
}
set.seed(1234)
co <- seq(0.3, 0.7, length=5)
X <- cbind(rep(co, each=5),
rep(co, times=5))
B <- 10
co <- seq(0, 1, length=B)
Z <- cbind(rep(co, each=B), rep(co, times=B))
dencovs <- cbind(spcov(Z),spcov(Z)[,3]) # ordered as reading raster image from left to right, bottom to top
dimnames(dencovs)[[2]][3:4] <- c("dencov1","dencov2")
denr.list <- vector("list",2)
for(i in 1:2){
denr.list[[i]] <- raster(
list(x=seq(0,1,length=10),
y=seq(0,1,length=10),
z=t(matrix(dencovs[,i+2],10,10,byrow=TRUE)))
)
}
B <- 20
co <- seq(0, 1, length=B)
Z <- cbind(rep(co, each=B), rep(co, times=B))
detcovs <- cbind(spcov(Z),spcov(Z)[,3]) # ordered as reading raster image from left to right, bottom to top
dimnames(detcovs)[[2]][3:4] <- c("detcov1","detcov2")
detcov.raster.list <- vector("list",2)
trapcovs <- matrix(0,J,2)
for(i in 1:2){
detr.list[[i]] <- raster(
list(x=seq(0,1,length=20),
y=seq(0,1,length=20),
z=t(matrix(detcovs[,i+2],20,20,byrow=TRUE)))
)
trapcovs[,i] <- extract(detr.list[[i]],X)
}
alpha0 <- -3
sigma <- 0.15
alphas <- c(1,-1)
beta0 <- 3
betas <- c(-1,1)
pixelArea <- (dencovs$y[2] - dencovs$y[1])^2
mu <- exp(beta0 + as.matrix(dencovs[,3:4])%*%betas)*pixelArea
EN <- sum(mu)
N <- rpois(1, EN)
pi <- mu/sum(mu)
s <- dencovs[sample(1:nrow(dencovs), size=N, replace=TRUE, prob=pi),1:2]
J <- nrow(X)
K <- 10
yc <- d <- p <- matrix(NA, N, J)
D <- e2dist(s,X)
loglam <- t(alpha0 - t((1/(2*sigma*sigma))*D*D) + as.vector(trapcovs%*%alphas))
p <- 1-exp(-exp(loglam))
for(i in 1:N) {
for(j in 1:J) {
yc[i,j] <- rbinom(1, K, p[i,j])
}
}
detected <- apply(yc>0, 1, any)
yscr <- yc[detected,]
ntel <- 5
nfixes <- 100
poss.tel <- which(s[,1]>0.2 & s[,1]<0.8 & s[,2]>0.2 & s[,2]<0.8)
stel.id <- sample(poss.tel,ntel)
stel <- s[stel.id,]
ytel <- matrix(NA,ntel,nrow(detcovs))
d <- e2dist(stel,detcovs[,1:2])
lam <- t(exp(1 - t((1/(2*sigma*sigma))*d*d) + as.vector(as.matrix(detcovs[,3:4])%*%alphas)))
for(i in 1:ntel){
ytel[i,] <- rmultinom(1,nfixes,lam[i,]/sum(lam[i,]))
}
Specify starting values and call mle2 function:
start1 <- list(alpha0=alpha0,sigma=sigma,alphas=alphas,betas=betas,n0=log(N-nrow(yscr)))
parnames(CSCR.RSF.intlik2.EXAMPLE) <- names(start)
out1 <- mle2(CSCR.RSF.intlik2.EXAMPLE,start=start1,method="SANN",optimizer="optim",
data=list(yscr=yscr,K=K,X=X,trapcovs=trapcovs,Gden=dencovs[,1:2],Gdet=detcovs[,1:2],
ytel=ytel,stel=stel,dencovs=as.matrix(dencovs[,3:4]),detcovs=as.matrix(detcovs[,3:4]))
)
