Skip to content

optim not giving correct minima

2 messages · Laura Forsberg White, Brian Ripley

Original
Laura Forsberg White
# 
Hello,

I am trying to use optim() on a function involving a summation.  My 
function basically is a thinned poisson likelihood.  I have two parameters 
and in most cases optim() does a fine job of getting the minima.  I am 
simulating my data based on pre specified parameters, so I know what I 
should be getting.  However when my true parameters fall in a particular 
range, optim() gives incorrect results.  I have generated a grid of 
parameter values and calculated my likelihood through those to see that the 
values that optim() gives is clearly not correct.  I can see that my 
likelihood does in fact have a unique maximum.  Any ideas why this might be?

The data given below was generated such that the true parameters should be 
(0.3001, -1.8971).  Here is an example piece of data and the function:

#function to maximize
likN_alpha <- function(params,N){

     thetas <- exp(params)

     k <- length(thetas)
     N <- c(rep(0,(k-1)),N)
     l <- length(N)

     lik <- 0

     for(i in (k):(l-1)){
         lambda <- thetas%*%N[i:(i-k+1)]
         lik <- -lambda + N[i+1]*log(lambda) + lik
     }

     return(-lik)
}

# data to maximize over
N <- c( 3, 3, 10, 19, 36, 54, 78,116,177, 265, 388, 598, 
890,1328,1910,2736,3982,5908,8471,12440,17964,26207,37688,54795,79270,114752,166594,242438, 
352753,512054)

#optim() command

optim(log(1.5*rep(1/2,2)),likN.alpha,N=N)

# If I use constrained optimization and a slightly different 
parameterization, then the results are fine, at least in this case, but not 
always.

Thanks for any help you might be able to offer!

laura
Brian Ripley
# 
Try the other methods that optim() supplies, and try supplying a 
analytical derviative (which looks easy enough).  On a problem like this I 
would expect to use BFGS with analytical derivatives.

If you don't want to do any of that, at least explore the control 
parameters.  It doesn't look to me as if you have attempted to scale the 
problem as the optim help page suggests you should.  Also, you say a 
`likelihood', but it is usual to maximize a log-likelihood. (Without 
knowing what you are trying to do in detail, I cannot tell if you are in 
fact using a log-likelihood.)
On Fri, 11 Nov 2005, Laura Forsberg White wrote: