Greetings,

I am struggling a bit with a non-linear regression. The problem is
described below with the known values r and D inidcated.
I tried to alter the start values but get always following error
message:

Error in nlsModel(formula, mf, start, wts):
  singular gradient matrix at initial parameter estimates
Calls: nls -> switch -> nlsModel

I might be missing something with regard to the different algorithms or
I just have to try again with some different start values. If anyone
finds some time to have a look at that, any advice would be very much
appreciated.


##Brice-Model
bricemod<-nls(log10(D) ~ log10(Do)*exp(((-4*pi*En*Na)*((ro/2)*(r-ro)^2
+(1/3)*(r-ro)^3))/(R*T)), start=list(Do=0.8, En=390,
ro=1.03),trace=TRUE)

Na<-6.0221415*10^23 # Avrogadro's number
T<-1010 # Temp in K
R<-8.3144 #Gas constant [J mol^-1 K^-1]

r<-data.matrix(PRr[c("r")])
     r
La 1.160
Ce 1.143
Pr  1.109
Nd 1.093
Sm1.079
Eu  1.066
Gd  1.053
Tb  1.040
Dy  1.027
Ho  1.015
Er   1.004
Tm  0.994
Yb   0.985
Lu   0.977


D<-data.matrix(PRr[c("D")])
     D
La 0.1806551
Ce 0.2703113
Pr 0.3757225
Nd 0.5271811
Sm 0.8665835
Eu 1.0812568
Gd 1.0612762
Tb 1.0726612
Dy 1.1679270
Ho 1.1910920
Er 1.1336938
Tm 1.1215107
Yb 0.9619603
Lu 0.8315467


Niklaus

-- 
Niklaus Hürlimann
Doctorant-(cand.PhD)

Université de Lausanne  
Institut de Minéralogie et Géochimie 
L'Anthropole 
CH-1015 Lausanne 
Suisse

E-mail: Niklaus.Hurlimann@unil.ch
Tel:+41(0)21 692 4452 

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