Hi,
While I agree with the comments about paying attention to parameter scaling, a
major issue here is that the default optimization algorithm, Nelder-Mead, is
not very good. It is unfortunate that the optim implementation chose this as
the "default" algorithm. I have several instances where people have come to me
with poor results from using optim(), because they did not realize that the
default algorithm is bad. We (John Nash and I) have pointed this out before,
but the R core has not addressed this issue due to backward compatibility
reasons.
There is a better implementation of Nelder-Mead in the "dfoptim" package.
?require(dfoptim)
mm_def1 <- nmk(par = par_ini1, min.perc_error, data = data)
mm_def2 <- nmk(par = par_ini2, min.perc_error, data = data)
mm_def3 <- nmk(par = par_ini3, min.perc_error, data = data)
print(mm_def1$par)
print(mm_def2$par)
print(mm_def3$par)
In general, better implementations of optimization algorithms are available in
packages such as "optimx", "nloptr". It is unfortunate that most na�ve users
of optimization in R do not recognize this. Perhaps, there should be a
"message" in the optim help file that points this out to the users.
Hope this is helpful,
Ravi
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