Hi, I am new to R. I don't have strong background of statistics. I am  
a student of Geotechnical Engineering. I tried to run a nonlinear  
regression for a three-variable function, that is

N = f(CSR, ev)   # N is a function of CSR and ev, and N = CSR/(A 
+B*CSR), wherer (A,B) are function of ev.

N, CSR and ev are observed in the experiments.
Following is my R script.

rm(list=ls())
library(nlme)

# assign data
N <- c 
(30.03,16.62,10.88,36.47,20.24,38.17,36.47,34.80,19.00,32.37,14.40,35.63 
, 
19.00,17.79,33.98,31.58,31.58,35.63,20.24,31.58,29.27,22.18,27.77,25.60, 
19.00,7.05,34.80,29.27,29.27,17.79,10.42,31.58,17.79,17.20,11.36,19.00,2 
9.27,12.33,22.18,22.18,14.40,31.58,19.00,9.52,33.17,13.87,19.00,21.52,11 
.36,22.84,9.96,6.68,20.88,9.96,11.84,20.24,19.61,17.20,17.20)

CSR <- c 
(0.25,0.42,0.12,0.438,0.49,0.42,0.47,0.46,0.24,0.45,0.37,0.46,0.337,0.36 
, 
0.334,0.346,0.399,0.44,0.246,0.33,0.413,0.23,0.45,0.45,0.44,0.106,0.333, 
0.256,0.345,0.44,0.153,0.348,0.23,0.25,0.122,0.183,0.201,0.128,0.23,0.24 
, 
0.129,0.438,0.228,0.111,0.409,0.14,0.24,0.20,0.22,0.22,0.152,0.094,0.131 
,0.123,0.155,0.28,0.204,0.149,0.193)

ev <- c 
(0.2,0.3,0.4,0.5,0.5,0.5,0.6,0.6,0.8,1,1.0,1.0,1.1,1.1,1.2,1.2,1.2,1.2,1 
. 
3,1.3,1.3,1.3,1.3,1.3,1.4,1.5,1.5,1.5,1.5,1.5,1.6,1.6,1.6,1.6,1.7,1.7,1. 
7,1.7,1.7,1.7,1.8,1.8,1.9,1.9,1.9,1.9,1.9,2.0,2.1,2.1,2.3,2.4,2.4,2.7,2. 
8,3.3,3.4,3.6,5.0)

# set the data frame
data1<- data.frame(cbind(N,CSR,ev))
# the initial values of parameters
para1.st <- c(a=75.4,b=165.9,c=-22.4,d=0,e=0.8,f=-0.28,g=0)
para2.st <- c(a=31.3,b=-176.9,c=53.41,d=0,e=75.2,f=-0.18,g=0)
# call nls funciton
try.control <- c(maxiter=100, minFactor=1/4096)
out <- nls(N~CSR/(1/(a+b*ev+c*(ev^2))+CSR/(d+e*exp(f*ev)))-g, data1,  
start=para1.st, control=try.control, trace=T)


The data is from experiments and the pattern of data is scatter quite  
a bit. I want to find the best fit coefficients (a,b,c,d,e,f,g) for  
the data.
I have two different sets of initial values for try. But in both  
cases I got error message of
"singular gradint"

What can I do for this error? Is there any other nonlinear regression  
model I can try?  This problem is kind of emergency. I really hope  
someone can help me out. Any comment is appreciated. Thanks a lot.



Niner
-----------------------------------------------
Yi-Min Huang
Civil & Environmental Engineering
U. of Washington
206-6165697


----------------------------------------------------
Niner, Seattle
ninerdummy@gmail.com




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