Sometimes having problems finding a minimum using optim(), optimize(), and nlm() (while searching for noncentral F parameters)

Ken Kelley <KKIII at Indiana.Edu> wrote

I have a problem that I have been unable to determine either the best
way to proceed and why the methods I'm trying to use sometimes fail. I'm
using the pf() function in an optimization function to find a
noncentrality parameter that leads to a specific value at a specified
quantile.

[SNIP]

I'm using three function [optim(), optimize(), and nlm()] to try and
accomplish the same goal (which was stated above). I believe that they
should all return the same value, and at times they do just that, but at
other times the methods return inappropriate results. I'll paste my code
that illustrates an example where all is well and one where things fail.

Perhaps uniroot() might be better
 Low.Lim.NC.F <- function(Lambda, alpha.lower, F.value, df.1, df.2) {
    pf(q=F.value, df1=df.1, df2=df.2, ncp=Lambda) - (1-alpha.lower)
 }
 uniroot(Low.Lim.NC.F, interval=c(0,50000), alpha.lower=0.025, df.1=5,
 df.2=200, F.value=12)

If you plot your example, the gradients are much steeper from above than
below, so nlm() works when the starting value is say 50.  In addition,
underflow in pf for more extreme values of lambda affect these more
general search algorithms.


| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
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