Poor performance of "Optim"

With respect, your statement that R's optim does not give you a reliable
estimator is bogus. As pointed out before, this would depend on when optim
believes it's good enough and stops optimizing. In particular if you stretch
out x, then it is plausible that the likelihood function will become flat
enough "earlier," so that the numerical optimization will stop earlier
(i.e., optim will "think" that the slope of the likelihood function is flat
enough to be considered zero and stop earlier than it will for more
condensed data). After all, maximum likelihood is a numerical method and
thus an approximation. I would venture to say that what you describe lies in
the nature of this method. You could also follow the good advice given
earlier, by increasing the number of iterations or decreasing the tolerance. 

However, check the example below: for all purposes it's really close enough
and has nothing to do with optim being "unreliable."

n<-1000
x<-rnorm(n)
y<-0.5*x+rnorm(n)
z<-ifelse(y>0,1,0)

X<-cbind(1,x)
b<-matrix(c(0,0),nrow=2)

#Probit
reg<-glm(z~x,family=binomial("probit"))

#Optim reproducing probit (with minor deviations due to difference in
method)
LL<-function(b){-sum(z*log(pnorm(X%*%b))+(1-z)*log(1-pnorm(X%*%b)))}
optim(c(0,0),LL)

#Multiply x by 2 and repeat optim
X[,2]=2*X[,2]
optim(c(0,0),LL)

HTH,
Daniel

What I tried is just a simple binary probit model.   Create a random data
and use "optim" to maximize the log-likelihood function to estimate the
coefficients.   (e.g. u = 0.1+0.2*x + e, e is standard normal.  And y = (u

0),  y indicating a binary choice variable)

If I estimate coefficient of "x", I should be able to get a value close to
0.2 if sample is large enough.  Say I got 0.18. 

If I expand x by twice and reestimate the model, which coefficient should
I get?  0.09, right?

But with "optim", I got something different.  When I do the same thing in
both Gauss and Matlab, I can exactly get 0.09, evidencing that the
coefficient estimator is reliable.  But R's "optim" does not give me a
reliable estimator.

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