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## Type I functional response function.
# A straight line with an intercept at zero, basically linear with respect to encouter rate
## Type I functional response ##
typeI <- function(X, a, T) {
if(is.list(a)){
coefs <- a
a <- coefs[['a']]
T <- coefs[['T']]
}
return(a*X*T) # Taken from Juliano 2001, eq. 10.1, pg 181. When h = 0 Ne=aNT/1
}
# typeI_fit: Does the heavy lifting
# data = The data from which to subsample. X and Y are drawn from here.
# samp = Provided by boot() or manually, as required
# start = List of starting values for items to be optimised. Can only be 'a'.
typeI_fit <- function(data, samp, start, fixed, boot=FALSE, windows=FALSE) {
# Setup windows parallel processing
fr_setpara(boot, windows)
samp <- sort(samp)
dat <- data[samp,]
out <- fr_setupout(start, fixed, samp)
try_typeI <- try(bbmle::mle2(typeI_nll, start=start, fixed=fixed, data=list('X'=dat$X, 'Y'=dat$Y), optimizer='optim'),
silent=T)
## Remove 'silent=T' for more verbose output
if (inherits(try_typeI, "try-error")){
# The fit failed...
if(boot){
return(out)
} else {
stop(try_typeI[1])
}
} else {
# The fit 'worked'
for (i in 1:length(names(start))){
# Get coefs for fixed variables
cname <- names(start)[i]
vname <- paste(names(start)[i], 'var', sep='')
out[cname] <- coef(try_typeI)[cname]
out[vname] <- vcov(try_typeI)[cname, cname]
}
for (i in 1:length(names(fixed))){
# Add fixed variables to the output
cname <- names(fixed)[i]
out[cname] <- as.numeric(fixed[cname])
}
if(boot){
return(out)
} else {
return(list(out=out, fit=try_typeI))
}
}
}
# typeI_nll
# Provides negative log-likelihood for estimations via bbmle::mle2()
# See Bowkers book for more info
# Generalised from rogersII_nll, should be OK (DP)
typeI_nll <- function(a, T, X, Y) {
if (a < 0) {return(NA)} # Zero would be a flat line, in this case, so is probably OK
prop.exp = typeI(X, a, T)/X
# The proportion consumed must be between 0 and 1 and not NaN
# If not then it must be bad estimate of a and h and should return NA
if(any(is.nan(prop.exp)) || any(is.na(prop.exp))){return(NA)}
if(any(prop.exp > 1) || any(prop.exp < 0)){return(NA)}
return(-sum(dbinom(Y, prob = prop.exp, size = X, log = TRUE)))
}
# Type I difference function
typeI_diff <- function(X, grp, a, T, Da) {
# return(a*X*T) # Taken from Juliano 2001, eq. 10.1, pg 181. When h = 0 Ne=aNT/1
return((a-Da*grp)*X*T)
}
# The NLL for the difference model... used by frair_compare()
typeI_nll_diff <- function(a, T, Da, X, Y, grp) {
if (a < 0) {return(NA)} # Zero would be a flat line, in this case, so is probably OK
prop.exp = typeI_diff(X, grp, a, T, Da)/X
# The proportion consumed must be between 0 and 1 and not NaN
# If not then it must be bad estimate of a and h and should return NA
if(any(is.nan(prop.exp)) || any(is.na(prop.exp))){return(NA)}
if(any(prop.exp > 1) || any(prop.exp < 0)){return(NA)}
return(-sum(dbinom(Y, prob = prop.exp, size = X, log = TRUE)))
}
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