# [R] solving multiple parameter starting values in nlm

Michael Rennie mrennie at utm.utoronto.ca
Tue Jul 8 23:14:35 CEST 2003

```Hi, there

At 12:28 AM 7/8/03 -0700, Spencer Graves wrote:
>           Did you work through the examples at the end of the "nlm"
> documentation?  The first example there shows that "nlm" expects a single
> vector argument over which f is to be minimized.  This suggests that your
> first construction should not work, while your second should be closer.

I've gone through and now attempted a number of varieties on this
theme.  Stated generally, the newest variation I am hung on is;

x<-NULL
Y<-NULL

q<-(x,y)

f <- function (q)
{
{
for i in (1:length(day))
{
.........I then use x and y in my loop for daily iterations, where each
element is dependent upon the value of the previous iteration, and obtain
values for c, d, and try to minimize the following function........
}
f <- ((a^2 -c^2)^2 + (b^2 - d^2)^2)^2/2 ; f
}
nlm (f, 1, r=1)

I've squared all the results, the differences, and the overall value as the
function to minimize such that the differences between the user input
values (a, b) and the model output (b,d) are exaggerated so as to obtain a
sufficient minimization.  This function works on it's own when performed
after the daily iteration loop, but it doesn't even get that far in this
version of the nlm loop.  Also, the loop with only my daily iterations
works fine (without the nlm loop), no warnings, all is good.

But, once I embed it within the loop for function f, my program stalls on
the daily iterations.  I get error messages that seem to indicate that it
isn't even going through the first iteration properly.

If, however, I code my input variables as q[1] and q[2] in the loop,
instead of x, y, it solves the loop correctly, but comes back with a
billion warnings that "the number of items to replace is not a multiple of
replacement length".  I think that it wants my q vector to be the same
length as the iterations in the daily loop, 365, but gets mad when it
isn't, because it possesses only 2 elements, (x ,y) or (q[1], q[2]).

As well, when I run the daily iteration loops OUTSIDE the nlm loop with the
q[1] and q[2] coding, I get the same error messages ("the number of items
to replace is not a multiple of replacement length").  Despite this, it
goes through the program and reports a solution.

My fear is that even though I am getting the right answers from the daily
loop in this last version, if I am getting errors, then I shouldn't just
simply ignore them and continue.  Or should I?  Are the errors simply a
result of a technicality?  Personally, I would feel better if I could do it
without them.

>           Also, did you try running your function by itself, checking to
> make sure it computed correctly?  The final line for the second function
> as I read it below appears OUTSIDE the function definition as a
> stand-alone expression to be executed once between the function
> definition and the "nlm" call.

Yes, or at least a modified version of it. see above.

>           Also, have you tried "optim"?  It seems to be more general and
> robust, requiring fewer assumptions to function.  The default method for
> "optim" does not require the function to be differentiable, while "nlm" does.

Yes, and "optim" is stalling in the same places and generating the same
errors as 'nlm'.

Any other thoughts or suggestions for what I'm doing wrong?

>hope this helps.  spencer graves
>
>Michael Rennie wrote:
>>Hi there
>>I am having trouble figuring out how to get an nlm function to report
>>estimates for two parameter values in an estimation.
>>The way I've got it goes something like this:
>>f <- function (q, r)
>>{
>>here, I have a second loop which uses q, r to give me values for c, d
>>below.  a and b are already specified; this loop is a mass-balance
>>function where I am trying to find values of q, r to give me c and d. I
>>want c and d (mass-balance model outputs) to approximate a and b (known
>>endpoints that I want the model to attain), respecitvely.  Thus, the
>>function I want to minimize is:
>>fu <- ((a^2 - c^2) + (b^2 - d^2))/2 ; fu
>>}
>>nlm (f, 1, r=1)
>>This doesn't return estimates for each parameter, and I get error
>>messages saying something like "repleaced missing value with maximum" or
>>something.  All I did here was try (and fail, obviously) to model my
>>needs against the examples given in help(nlm), but they are using vectors
>>as inputs, and I only need 2 values input, and 2 returned.
>>I've also tried specifying the function as
>>f <- function (q)
>>{
>>mass-balance loop
>>}
>>fu <- ((a^2 - c^2) + (b^2 - d^2))/2 ; fu
>>nlm(f, c(1,1))
>>Specifying 1 as the starting values, and coding q[1] and q[2] in my mass
>>balance loop instead of q, r.
>>But this doesn't work either, and I get messages that I think are
>>indicating that my mass balance loop isn't computing properly ("number of
>>items to replace is not a multiple of replacement length"- an error I
>>don't get when I run the mass-balance loop outside the nlm function and
>>just specify q, r).
>>Does anyone know how to specify two parameters in the function, and ask
>>for estimates of both back from nlm? Alternatively, any hunches on how to
>>make this thing do what I want it to?
>>Thanks,
>>Mike
>

Michael Rennie
M.Sc. Candidate
University of Toronto at Mississauga
3359 Mississauga Rd. N.
Mississauga, ON  L5L 1C6
Ph: 905-828-5452  Fax: 905-828-3792

```