[R] Need for optim() resistant to error on the fit criteria.

[Marc Girondot]

Hi,

I try to fit parameters based on the comparison between a stochastic 
model that uses these parameters and observed data.
The problem is that two runs with the same set of parameters will 
produce a fitting criteria slightly different.
I found that optim() is highly sensitive to such a situation and 
produces completly wrong result.
I reproduce this situation below.
v is a set of 50 "observed" values
par is the set of parameters to be fitted
fitNorm returns the -Ln L of the observations based on a Gaussian 
distribution
fitNorm_error returns the -Ln L of the observations based on a Gaussian 
distribution + a small error

Example of optim() result:
with fitNorm
final  value 215.918650
converged
$par
[1] 156.27980  18.16392 (compared to 157.5, 18.5)

with fitNorm_error
final  value 271.661187
converged
$par
[1] 169.98441  88.81387 (compared to 157.5, 18.5)

So the question: is there another solution for a fitting procedure that 
is more resistant to change in fit criteria ?

Thanks a lot,

Marc




#The likelihood function that returns -Ln L of the data
fitNorm<-function(para) {
     return(-sum(dnorm(v, para[1], para[2], log=TRUE)))
}

#The likelihood function that returns -Ln L of the data with a slight error
fitNorm_error<-function(para) {
     return(-sum(dnorm(v, para[1], para[2], log=TRUE))+rnorm(1, 0, 0.1))
}


#Generate 50 random number from a Gaussian distribution
v<-rnorm(50, 157.5, 18.5)

par<-c(100, 10)

optim(par, fitNorm, method="BFGS", hessian=FALSE, 
control=list(maxit=500, trace=1))


optim(par, fitNorm_error, method="BFGS", hessian=FALSE, 
control=list(maxit=500, trace=1))


-- 
__________________________________________________________
Marc Girondot, Pr

Laboratoire Ecologie, Systématique et Evolution
Equipe de Conservation des Populations et des Communautés
CNRS, AgroParisTech et Université Paris-Sud 11 , UMR 8079
Bâtiment 362
91405 Orsay Cedex, France

Tel:  33 1 (0)1.69.15.72.30   Fax: 33 1 (0)1.69.15.73.53
e-mail: marc.girondot at u-psud.fr
Web: http://www.ese.u-psud.fr/epc/conservation/Marc.html
Skype: girondot