# [R] Fitting data with optim or nls--different time scales

Spencer Graves spencer.graves at pdf.com
Thu Aug 10 10:40:59 CEST 2006

<see in line>

Leslie Chavez wrote:
> Hi,
>
> I have a system of ODE's I can solve with lsoda.
>
> Model=function(t,x,parms)
> {
>     #parameter definitions
>     lambda=parms[1]; beta=parms[2];
>     d = parms[3]; delta = parms[4];
>      p=parms[5];    c=parms[6]
>
>       xdot[1] = lambda - (d*x[1])- (beta*x[3]*x[1])
>       xdot[2] = (beta*x[3]*x[1]) - (delta*x[2])
>       xdot[3] = (p*x[2]) - (c*x[3])
>
>     return(list(xdot))
> }
>
> I want to fit the output out[,4] to experimental data that is only
> available on days 0, 7, 12, 14, 17, and 20. I don't know how to set up
> optim or nls so that it takes out[,4] on the appropriate day, but still
> runs lsoda on a time scale of 0.01 day.
>
> Below is the function I've been using to run 'optim', at the
> course-grained time scale:
>
SG:  What about the following:

Modelfit=function(s) {
parms[1:4]=s[1:4];
times=c(0,7,12,14,17,20,25)
lsodaTimes <- seq(min(times),max(times), by=0.01)
out=lsoda(x0,lsodaTimes,Model,parms)
obsTimes <- (100*times-1)
mse=mean((log10(out[obsTimes,4])-log10(i(times)))^2)
#	cat(times)
return(mse)
}

Your example is not self contained, so obviously I haven't tried this
with it.  However, something of this nature should work fine, I believe.
Something similar but different should also work, I believe, with
'nls';  this would give you access to many helper functions (see
"methods(class='nls')").  If 'nls' bombed on me, I'd then try 'optim' as
it is less brittle.  Then I might use the output of 'optim' as initial
values for 'nls' to get confidence intervals etc.

hope this helps.
Spencer Graves

> #x0=c(T0,I0,V0)
> x0=c(2249,0,1)
> #parms(lambda, beta, d, delta, p, c)
> parms[5:6]=c(1.0,23)
>
> s0=c(49994,8456,6.16E-8,0.012) #initial values
>
> fit=optim(s0,Modelfit)
>
> Right now, lsoda is being run on too course-grained a time scale in the
> function Modelfit. Most examples of optim and nls I have found compare
> two data sets at the same times, and run lsoda on the time scale the
> data is available at, but I would like to run lsoda at a finer scale, and
> only compare the appropriate time points with the experiment.  I have also
> tried using nls, but I have the same problem. Does anyone have
> suggestions?
>
> Thank you very much,
>
> Leslie
>
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