[R] L-BFGS-B needs finite values of 'fn'

[Prof Brian Ripley]

On Tue, 24 Jun 2008, Jinsong Zhao wrote:

> Hi,
>
> When I run the following code,
>
> r <- c(3,4,4,3,5,4,5,9,8,11,12,13)
> n <- rep(15,12)
> x <- c(0, 1.1, 1.3, 2.0, 2.2, 2.8, 3.7, 3.9, 4.4, 4.8, 5.9, 6.8)
> x <- log10(x)

So x[1] = -Inf

> fr <- function(c, alpha, beta) {
>  P <- c + (1-c) * pnorm(alpha + beta * x)
>  P <- pmax(pmin(P,1),0)
>  -(sum(log(choose(n,r))) + sum(r * log(P)) + sum((n -r)* log(1-P)))
> }
> fit <- mle((fr), start = list(c =0.2, alpha = 0, beta =0.1), method =
> "L-BFGS-B")
>
> I got:
>
> Error in optim(start, f, method = method, hessian = TRUE, ...) :
>  L-BFGS-B needs finite values of 'fn'
>
> When I change "L-BFGS-B" to "BFGS" or anything else that optim()
> support, there's no any error message.
>
> What's wrong?

What the message says.  Your fr() function is returning non-finite values. 
Look at what happens if P is 0 or 1 for example.  You seem to need 0 < c < 
1, and you have not imposed that constraint.  Adding a trace tp print 
c(c, alpha, beta) I got

[1] 0.2 0.0 0.1
[1] 0.201 0.000 0.100
[1] 0.199 0.000 0.100
[1] 0.200 0.001 0.100
[1]  0.200 -0.001  0.100
[1] 0.200 0.000 0.101
[1] 0.200 0.000 0.099
[1] -0.63692943 -0.54093515  0.01670358
Error in optim(start, f, method = method, hessian = TRUE, ...) :
   L-BFGS-B needs finite values of 'fn'

and other methods also give negative 'c' (and backtrack).  There are also 
problems if beta < 0 (as c + (1-c) * pnorm(alpha + beta * x) = 1 for x = 
-Inf).  So

fit <- mle((fr), start = list(c =0.2, alpha = 0, beta =0.1),
            method = "L-BFGS-B", lower=c(0, -Inf, 0), upper = c(1, Inf, Inf))

works.

There is no point in using "L-BFGS-B" in a 3-parameter problem unless you 
do impose constraints.

Also, dbinom() will give a more stable way to compute a binomial 
log-likelihood.

> Any suggestions will be appreciated.
>
> Jinsong

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
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