Re: [R] problems with optim, "for"-loops and machine precision

From: <Setzer.Woodrow_at_epamail.epa.gov>
Date: Wed 10 Jan 2007 - 16:57:25 GMT


Without more detail - a reproducible example - it is hard to give you concrete advice.

I wonder if the functions NLL23 and NLL21 depend on numerical solutions of a system of ODEs, since you invoke the odesolve package? If so, try switching to the Nelder-Mead optimizer, enforcing the parameter constraints using transformation. Probably you are using the finite difference derivatives calculated internally to optim for the gradient information used in the L-BFGS-B optimizer. These can be unstable when based on numerical solutions of odes, causing the optimizer to fail, or sometimes to converge to a non-optimal point.

Some other points:
- you cannot change machine precision by changing values in .Machine. To change the number of digits printed, use options(digits=8). - use 'library()' instead of 'require()', unless you need to use the return value from 'require()'

R. Woodrow Setzer, Ph. D.
National Center for Computational Toxicology US Environmental Protection Agency
Mail Drop B205-01/US EPA/RTP, NC 27711
Ph: (919) 541-0128 Fax: (919) 541-1194

                                                                        
             Simon Ruegg                                                
             <s.ruegg@access.                                           
             unizh.ch>                                               To 
             Sent by:                 r-help@stat.math.ethz.ch          
             r-help-bounces@s                                        cc 
             tat.math.ethz.ch                                           
                                                                Subject 
                                      [R] problems with optim,          
             01/10/2007 07:18         "for"-loops and machine precision 
             AM                                                         
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        




Dear R experts,

I have been encountering problems with the "optim" routine using "for" loops. I am determining the optimal parameters of several nested models by
minimizing the negative Log-Likelihood (NLL) of a dataset.

The aim is to find the model which best describes the data. To this end, I
am simulating artificial data sets based on the model with the least number
of parameters (6) and the parameters determined with the field data. For each artificial set I estimate the parameters of the model with 6 parameters
and the next more complex model with 7 parameters (two of these parameters
are equal in the 6-parameter model) by minimizing the corresponding NLL with
"optim". In theory the 7-parameter model should fit the data either
equally
or better than the 6-parameter model. Therefore the difference of the minimal NLLs should be 0 or larger.

For 500 data sets I use the following code:

require(odesolve)

res=matrix(nrow=500,ncol=18)

colnames(res)=c("a_23","beta_23","mu_23","d_23","I_23","M_23","NLL_23",

"a_21","beta_21","mu_21","e_21","d_21","I_21","M_21","NLL_21",

            "NLL23_min_21","conv23","conv21")

for (s in 1:500)

{

assign("data",read.table(paste("populations/TE23simset_",s,".txt",sep="")),e

nv=MyEnv) #reading a data set

  M23=optim(rep(0.1,6),NLL23,method="L-BFGS-B",lower=0,

      upper=c(Inf,Inf,Inf,Inf,1,1),control=c(maxit=150))

  if (M23$convergence==0)

    {

       M21=optim(rep(0.1,7),NLL21,method="L-BFGS-B",lower=0,

            upper=c(Inf,Inf,Inf,Inf,Inf,1,1),control=c(maxit=150))

    }

      res[s,1]=M23$par[1]

      res[s,2]=M23$par[2]

      res[s,3]=M23$par[3]

      res[s,4]=M23$par[4]

      res[s,5]=M23$par[5]

      res[s,6]=M23$par[6]

      res[s,7]=M23$value

      res[s,8]=M21$par[1]

      res[s,9]=M21$par[2]

      res[s,10]=M21$par[3]

      res[s,11]=M21$par[4]

      res[s,12]=M21$par[5]

      res[s,13]=M21$par[6]

      res[s,14]=M21$par[7]

      res[s,15]=M21$value

      res[s,16]=M23$value-M21$value

      res[s,17]=M23$convergence

      res[s,18]=M21$convergence

      write.table(res,"compare23_21TE061221.txt")

      rm(M23,M21)

   }

}

For some strange reason the results do not correspond to what I expect: about 10% of the solutions have a difference of NLL smaller than 0. I have
verified the optimisation of these results manually and found that a minimal
NLL was ignored and a higher NLL was returned at "convergence". To check what was happening I inserted a printing line in the NLL function to print
all parameters and the NLL as the procedure goes on. To my surprise
"optim"

then stopped at the minimal NLL which had been ignored before. I have then
reduced the machine precision to .Machine$double.digits=8 thinking, that the
printing was slowing down the procedure and by reducing the machine precision to speed up the calculations. For an individual calculation this
solved my problem. However if I implemented the same procedure in the loop
above, the same impossible results occurred again.

Can anyone tell me where I should be looking for the problem, or what it is
and how I could solve it?

Thanks a lot for your help

Sincerely

Simon


Simon Ruegg

Dr.med.vet., PhD candidate

Institute for Parasitology

Winterthurstr. 266a

8057 Zurich

Switzerland

phone: +41 44 635 85 93

fax: +41 44 635 89 07

e-mail: s.ruegg@access.unizh.ch

             [[alternative HTML version deleted]]



R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.

R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu Jan 11 04:03:45 2007

Archive maintained by Robert King, hosted by the discipline of statistics at the University of Newcastle, Australia.
Archive generated by hypermail 2.1.8, at Wed 10 Jan 2007 - 17:30:30 GMT.

Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help. Please read the posting guide before posting to the list.