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

From: Ben Bolker <bolker_at_zoo.ufl.edu>
Date: Mon, 30 Jul 2007 08:05:30 -0400

  [sent this last night, may have bounced, resending]

  With R 2.5.1 ...

  "L-BFGS-B" behaves differently from all of the other optim() methods, which 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 that was originally fitted with "L-BFGS-B".

 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.

  Ben Bolker


## 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))

## same again with method="L-BFGS-B"

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

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)

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

## 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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