stuck with maximum likelihood problem

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Here is my situation in a simple description:

I have an equation that has one parameter and 3 data variables. ?I need to
get R to determine the parameter value that maximizes the sum calculated
from the equation.

I know this is simple problem but my search into functions of R got me
confused. ?I think I should use the optim function but I also read about the
trust function. ?I found some very useful examples for the optim function
but they related to specific distributions (i.e. normal, poisson)

Your question is pretty vague ...

  Suppose you define a function  objfun() that takes the parameter as
its first argument (for simplicity, let's say that it just uses the
values of the
data drawn from the global workspace) so that objfun(p) returns the value
you are trying to maximize.

  Then

  optim(startval,fn=objfun,control=list(fnscale=-1))

  should find the value of the parameter that maximizes the function
(by default optim() does minimization: the fnscale=-1 option makes
it do maximization instead
Have you considered doing the math needed to solve the score equation? 
You will need to solve a single nonlinear equation

        g(theta) = 0

If you cant do this analytically you should be able to transform it to 
the form

        theta = h(theta)

and then iterate on h or h-inverse from a suitable starting value to 
find a fixed point.

Murray Jorgensen
I know this is a mixed effect model email list and I apologize if I annoy
anyone.  I figured since I was already a member of this list I could try my
question here first.  Also, I have received VERY helpful responses from this
list in the past and I am hoping to repeat this.

Here is my situation in a simple description:

I have an equation that has one parameter and 3 data variables.  I need to
get R to determine the parameter value that maximizes the sum calculated
from the equation.

I know this is simple problem but my search into functions of R got me
confused.  I think I should use the optim function but I also read about the
trust function.  I found some very useful examples for the optim function
but they related to specific distributions (i.e. normal, poisson)

Any advice would be greatly appreciated.

Mike

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Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
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