Why the mle function can not run with lower and upper bound? - r

Question

I tried to use mle to estimate the parameters for the negative binomial distribution. Here is my code.
library(stats4)
library(bbmle)
library(MASS)
b=rnbinom(n=1000, size=3, prob=0.1)
LL2 <- function(size, prob) {
R = dnbinom(b, size, prob, log = TRUE)
-sum(R)
}
When I set the mle function with lower and upper bound, I got
stats4::mle(LL2, start = list(size = 3, prob = 0.1),lower = c(-Inf,-Inf),upper = c(Inf,Inf))
Error in optim(start, f, method = method, hessian = TRUE, lower = lower, :
L-BFGS-B needs finite values of 'fn'
When I removed the bounds
stats4::mle(LL2, start = list(size = 3, prob = 0.1))
Call:
stats4::mle(minuslogl = LL2, start = list(size = 3, prob = 0.1))
Coefficients:
size prob
3.0467857 0.1037522
However, if I change the bounds to a finite value, the error is still there.
I was wondering why this happened? Is that because the L-BFGS-B method can not handle with bounds settings?
Any comments will be appreciated.

Answer 1

I ran your setup code with set.seed(101).
Create an instrumented version of the score function so we can see where the optimizer is going:
LL2 <- function(size, prob) {
R = dnbinom(b, size, prob, log = TRUE)
res <- -sum(R)
cat(size,prob,res,"\n")
res
}
stats4::mle(LL2, start = list(size = 3, prob = 0.1),lower = c(-Inf,-Inf),upper = c(Inf,Inf))
## 3 0.1 4085.146
## 3.001 0.1 4085.166
## 2.999 0.1 4085.127
## 3 0.101 4084.767
## 3 0.099 4085.858
## 2.964666 1.099376 NaN
Error in optim(start, f, method = method, hessian = TRUE, lower = lower, :
L-BFGS-B needs finite values of 'fn'
In addition: Warning message:
In dnbinom(b, size, prob, log = TRUE) : NaNs produced
The first 5 steps are the evaluation of initial value and of the finite difference approximation of the derivatives. The very next optimization step takes us to prob = 1.099, which gives us an NaN result (we need 0 < prob < 1). L-BFGS-B is much more finicky than the other optimizers about non-finite values; most of the others treat non-finite results as "bad" and try something sensible.
You could set the lower bound to 0 for size and bounds (0,1) for prob ... (I tried it and it seems to work). You do have to be a little bit careful with L-BFGS-B - it doesn't always respect the bounds when it is calculating the finite-difference approximation, so e.g. if values <= 0 will give non-finite results you may need to set the lower bound slightly above 0 (e.g. 0.002, since the default finite-difference epsilon is 0.001).