[Rd] behavior of L-BFGS-B with trivial function triggers bug in stats4::mle

From: Ben Bolker <bolker_at_zoo.ufl.edu>
Date: Sun, 29 Jul 2007 18:04:23 -0400

   With the exception of "L-BFGS-B", all of the other optim() methods return the value of the function when they are given a trivial function (i.e., one with no variable arguments) to optimize. I don't think this is a "bug" in L-BFGS-B (more like a response to an undefined condition), but it leads to a bug in stats4::mle --  a spurious error saying that a better fit has been found during profiling if one tries to profile a 1-parameter model.

  I haven't dug quite all the way to the bottom of this yet, but the attached code will clearly show the problem.

  In the version of mle that I've built (which has gotten some ugly bells and whistles added) I added a check which would be more or less equivalent to check if length(start)==0 and then setting

    oout <- list(par=start, value=f(start),

                 hessian = matrix(numeric(0),0,0)
 

 or something along those lines.

  Or one could change L-BFGS-B to behave the same as the other methods.

 cheers
   Ben Bolker



library(stats4)

## using example from ?mle
x <- 0:10
y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8) ll <- function(ymax=15, xhalf=6)
  -sum(stats::dpois(y, lambda=ymax/(1+x/xhalf), log=TRUE))

## fix one parameter to get 1D profile
fit2 <- mle(ll, fixed=list(xhalf=6))
profile(fit2)

## same again with method="L-BFGS-B"
fit3 <- mle(ll, fixed=list(xhalf=6),method="L-BFGS-B") profile(fit3)

ll0 <- function(zzz) {
  ymax <- 15
  xhalf <- 6
  -sum(stats::dpois(y, lambda=ymax/(1+x/xhalf), log=TRUE)) }

## try mle() with all-fixed parameters with various methods ...
methods = eval(formals(optim)$method)
sapply(methods,

       function(m) {
         -logLik(mle(ll, start=list(ymax=15,xhalf=6),
                     fixed=list(ymax=15,xhalf=6),method=m))
       })

## Nelder-Mead BFGS CG L-BFGS-B SANN
## 3.389441e+01 3.389441e+01 3.389441e+01 5.048277e-270 3.389441e+01


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