R: Error with Nelder-Mead optimization to select starting values - r

Question

The data can be found here
library(nlme)
library(dfoptim)
dat0 <- read.table("aids.dat2",head=T)
dat1 <- dat0[dat0$day<=90, ] # use only first 90-day data
dat2 <- dat1[!apply(is.na(dat1),1,any),] # remove missing data
aids.dat <- groupedData(lgcopy ~ day | patid, data=dat2)
aids.dat$log10copy = log10(aids.dat$lgcopy)
myfun2 <- function(arg){
s.p1 <- arg[1]
s.b1 <- arg[2]
s.p2 <- arg[3]
s.b2 <- arg[4]
model = nlme(log10copy ~ exp(p1-b1*day) + exp(p2-b2*day),
fixed = list(p1 ~ 1, b1 ~ 1, p2 ~ 1, b2 ~ 1),
random = list(patid = pdDiag(list(p1 ~ 1, b1 ~ 1, p2 ~ 1, b2 ~ 1))),
start = list(fixed = c(p1 = s.p1, b1 = s.b1, p2 = s.p2, b2 = s.b2)),
data =aids.dat)
return(model$logLik)
}
nmkb(fn = myfun2, par = c(10,0.5,6,0.005), lower = c(5, 0.1, 5, 0.001), upper = c(15, 1, 10, 0.1))
Running the above code, I run into several errors:
Error in nlme.formula(log10copy ~ exp(p1 - b1 * day) + exp(p2 - b2 * day), :
step halving factor reduced below minimum in PNLS step
In addition: Warning message:
In nlme.formula(log10copy ~ exp(p1 - b1 * day) + exp(p2 - b2 * day), :
Singular precision matrix in level -1, block 1
The model fits fine with the staring values from par = c(10,0.5,6,0.005). However, I think as the random algorithm starts using other starting values in lower = c(5, 0.1, 5, 0.001), upper = c(15, 1, 10, 0.1) the nlme call runs into the above problems because it's so sensitive to starting values. As a result, the nmkb call never amounts to anything.
Is there a way to circumvent this?

Answer 1

The model log-liklihood needs to be maximized, but many optimization procedures in R gives minimization result. So the function to be optimized has to be the negative log-likelihood. So it should look like this:
myfun2 <- function(arg){
s.p1 <- arg[1]
s.b1 <- arg[2]
s.p2 <- arg[3]
s.b2 <- arg[4]
model = nlme(log10copy ~ exp(p1-b1*day) + exp(p2-b2*day),
fixed = list(p1 ~ 1, b1 ~ 1, p2 ~ 1, b2 ~ 1),
random = list(patid = pdDiag(list(p1 ~ 1, b1 ~ 1, p2 ~ 1, b2 ~ 1))),
start = list(fixed = c(p1 = s.p1, b1 = s.b1, p2 = s.p2, b2 = s.b2)),
data =aids.dat)
return(-model$logLik)
}
And although there are still many warnings, there is no more error on my machine, and the algorithm converges successfully.
$par
[1] 13.460199068 0.848526199 7.764024099 0.001513636
$value
[1] -358.6631
$feval
[1] 197
$restarts
[1] 0
$convergence
[1] 0
$message
[1] "Successful convergence"
Warning messages:
1: In nlme.formula(log10copy ~ exp(p1 - b1 * day) + exp(p2 - b2 * day), :
Singular precision matrix in level -1, block 1