[R] maximum likelihood with constraints in R

[Ben Bolker]

Plat, H.J. <H.J.Plat <at> uva.nl> writes:

> There is lots of information about maximum likelihood estimation in R.
> However, I didn't came across anything about maximum likelihood
> with constraints.
> For example, estimation of parameters k(1) to k(20) with
> maximum likelihood, where sum(k(i)) = 0.

  If the individual parameters don't need to be constrained,
then this is easy to do by estimating parameters k(1) to k(19)
and setting k(20) to -sum_{i=1}^19 k(i).  e.g. something like

objfun <- function(k) {  ## k is a vector parameters 1 to 19
   kvec <- c(k,-sum(k))
   ### ... compute and return negative log-likelihood based on kvec ...
}

optim(fn=objfun,par=[starting values])

  If you need "box constraints" (individual parameters independently
bounded above and below) you can use method="L-BFGS-B" in optim.

  Ben Bolker