[R] nls & fitting
Lorenzo Isella
lorenzo.isella at gmail.com
Sun May 21 22:20:16 CEST 2006
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
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