R help - Nov 2005 - optim

Hello:

I am trying to use optim() to estimate the maximum likelihood of a 
function a*x^b = y.
Unfortunately, I always get the error, that there is no default value for b.

Could you give me an example, on how to correctly optimize this function 
with input data x<-c(1,3,11,14).

Thanks a lot,

Adrienne

-- 
***********************************************************************
Adrienne Gr??t-Regamey          			
LEP, Landscape and Environmental Planning,
HIL H 31.2, ETH H??nggerberg
CH - 8093 Z??rich

Phone: +41/1/633'30'02 or +41/31/971'53'74
Fax:   +41/1/633'10'84 	
http://lep.ethz.ch/

Adrienne Gret-Regamey wrote:
> Hello:
> 
> I am trying to use optim() to estimate the maximum likelihood of a 
> function a*x^b = y.
> Unfortunately, I always get the error, that there is no default value for
b.
> 
> Could you give me an example, on how to correctly optimize this function 
> with input data x<-c(1,3,11,14).
> 
> Thanks a lot,
> 
> Adrienne
> 
Problems such as these will have more meaningful responses if you post 
an example (see the posting guide). What's being parameterized here? a 
or b or both? If just 'a', then fix 'b' at the desired value. If
both,
then give optim a starting value. And what is 'y'?

fn <- function(par, y, x) {
   a <- par[1]
   b <- par[2]
   sum((y - a * x^b)^2)
}

x <- c(1, 3, 11, 14)
y <- exp(rnorm(length(x)))
## y ~ a * x^b
## log(y) ~ log(a) + b * log(x)
v <- coef(lm(log(y) ~ log(x)))
optim(c(exp(v[1]), v[2]), fn, y = y, x = x)

Again, I may be way off. Please provide an example if this doesn't cover 
what you need. And define all the variables need to run your script.

--sundar