# [R] nls & fitting

From: Lorenzo Isella <lorenzo.isella_at_gmail.com>
Date: Mon 22 May 2006 - 06:20:16 EST

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

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