[R] nls & fitting

[Lorenzo Isella]

Dear All,
I may look ridiculous, but I am puzzled at the behavior of the nls with
a fitting I am currently dealing with.
My data are:

       x         N
1   346.4102 145.428256
2   447.2136 169.530634
3   570.0877 144.081627
4   721.1103 106.363316
5   894.4272 130.390552
6  1264.9111  36.727069
7  1788.8544  52.848587
8  2449.4897  25.128742
9  3464.1016   7.531766
10 4472.1360   8.827367
11 6123.7244   6.600603
12 8660.2540   4.083339

I would like to fit N as a function of x according to a function
depending on 9 parameters (A1,A2,A3,mu1,mu2,mu3,myvar1,myvar2,myvar3),
namely
N ~
(log(10)*A1/sqrt(2*pi)/log(myvar1)*exp(-((log(x/mu1))^2)/2/log(myvar1)/log(myvar1))

+log(10)*A2/sqrt(2*pi)/log(myvar2)*exp(-((log(x/mu2))^2)/2/log(myvar2)/log(myvar2))

+log(10)*A3/sqrt(2*pi)/log(myvar3)*exp(-((log(x/mu3))^2)/2/log(myvar3)/log(myvar3)))

(i.e. N is to be seen as a sum of three "bells" whose parameters I need
to determine).


So I tried:
out<-nls(N ~ 
(log(10)*A1/sqrt(2*pi)/log(myvar1)*exp(-((log(x/mu1))^2)/2/log(myvar1)/log(myvar1))

+log(10)*A2/sqrt(2*pi)/log(myvar2)*exp(-((log(x/mu2))^2)/2/log(myvar2)/log(myvar2))

+log(10)*A3/sqrt(2*pi)/log(myvar3)*exp(-((log(x/mu3))^2)/2/log(myvar3)/log(myvar3)))
 ,start=list(A1 = 85,
A2=23,A3=4,mu1=430,mu2=1670,mu3=4900,myvar1=1.59,myvar2=1.5,myvar3=1.5  )
,algorithm = "port"
,control=list(maxiter=20000,tol=10000)
,lower=c(A1=0.1,A2=0.1,A3=0.1,mu1=0.1,mu2=0.1,mu3=0.1,myvar1=0.1,myvar2=0.1,myvar3=0.1)
)

getting the error message:
Error in nls(N ~ (log(10) * A1/sqrt(2 * pi)/log(myvar1) *
exp(-((log(x/mu1))^2)/2/log(myvar1)/log(myvar1)) +  :
        Convergence failure: singular convergence (7)


I tried to adjust tol & maxiter, but unsuccessfully.
If I try fitting N with only two "bells", then nls works:

out<-nls(N ~ 
(log(10)*A1/sqrt(2*pi)/log(myvar1)*exp(-((log(x/mu1))^2)/2/log(myvar1)/log(myvar1))

+log(10)*A2/sqrt(2*pi)/log(myvar2)*exp(-((log(x/mu2))^2)/2/log(myvar2)/log(myvar2))
        )
 ,start=list(A1 = 85, A2=23,mu1=430,mu2=1670,myvar1=1.59,myvar2=1.5  )
,algorithm = "port"
,control=list(maxiter=20000,tol=10000)
,lower=c(A1=0.1,A2=0.1,mu1=0.1,mu2=0.1,myvar1=0.1,myvar2=0.1)
)

 out
Nonlinear regression model
  model:  N ~ (log(10) * A1/sqrt(2 * pi)/log(myvar1) *
exp(-((log(x/mu1))^2)/2/log(myvar1)/log(myvar1)) +      log(10) *
A2/sqrt(2 * pi)/log(myvar2) *
exp(-((log(x/mu2))^2)/2/log(myvar2)/log(myvar2)))
   data:  parent.frame()
        A1         A2        mu1        mu2     myvar1     myvar2
 84.920085  40.889968 409.656404 933.081936   1.811560   2.389215
 residual sum-of-squares:  2394.876

Any idea about how to get nls working with the whole model?
I had better luck with the nls.lm package, but it does not allow to
introduce any constrain on my fitting parameters.
I was also suggested to try other packages like optim to do the same
fitting, but I am a bit unsure about how to set up the problem.
Any suggestions? BTW, I am working with R Version 2.2.1

Lorenzo