Nonlinear regression in R shows error - r

Question

I am using the R function nlsLM from the package minpack.LM and I have the following error.
I generate my own signal with noise, so I know all parameters, which I'am trying to find doing regression analysis using the same function, I've used to generate signal.
The problem is, that nlsLM function runs fine, and it even could find right parameters values, but at last, when it finds them, error appear like this:
It. 23, RSS = 14.4698, Par. = 42.6727 0.78112 1 65.2211 15.6065 1
It. 24, RSS = 14.4698, Par. = 42.671 0.781102 1 65.2212 15.6069 1
Error in stats:::nlsModel(formula, mf, start, wts) :
singular gradient matrix at initial parameter estimates
And I do not know what to do.
Please explain what it could be, and how I could solve it!
Additional information:
#This is how i generate my signal (it is convolution of gaussian with exp(-kt)
set.seed(100)
Yexp=sim_str_exp(error=10)
time=Yexp[[1]]
y=Yexp[[2]]
dataset_nls=data.frame(time,y)
start=c(tau1=.5,beta1=.5,exp_A1=.5,gaus_pos=.5,gaus_width=.5,gaus_A=0.5)
lower=c(tau1=0.01,beta1=0.01,exp_A1=0.01,gaus_pos=0.01,gaus_width=0.01,gaus_A=0.01)
upper=c(tau1=100,beta1=1,exp_A1=1,gaus_pos=100,gaus_width=850,gaus_A=1)
#here i do fitting
FIT=nlsLM(y ~ str_exp_model(time,tau1,beta1,exp_A1,gaus_pos,gaus_width,gaus_A),data=dataset_nls,start=start,lower=lower,upper=upper,trace=TRUE,algorithm="LM",na.action=na.pass,control=nls.lm.control(maxiter=200,nprint=1))
#Model_function
str_exp_model<-function(time, tau1,beta1,exp_A1,gaus_pos,gaus_width,gaus_A){
F_gen_V<-vector(length=length(time))
F_gaus_V=vector(length=length(time))
F_exp_V=vector(length=length(time))
for (i in 1:length(time)) {
F_gaus_V[i]=gaus_A*exp(-2.77*((i-gaus_pos)/gaus_width)^2)
F_exp_V[i]=exp_A1*exp(-1*(i/tau1)^beta1)
}
convolve(F_gaus_V, F_exp_V,FALSE)
}
function for signal generation
sim_str_exp<- function(num_points=512,time_scale=512,tau1=45,beta1=.80,exp_A1=1,gaus_pos=65,
gaus_width=15, gaus_A=1,Y0=0, error=2.0, show_graph=TRUE, norm="False"){
F_gen_V<-vector(length=num_points)
time_gen_V<-vector(length=num_points)
F_gaus_V=vector(length=num_points)
F_exp_V=vector(length=num_points)
ts=time_scale/num_points
sigma=vector(length=num_points)
for (i in 1:num_points) {
F_gaus_V[i]=gaus_A*exp(-2.77*((i*ts-gaus_pos)/gaus_width)^2)
F_exp_V[i]=exp_A1*exp(-1*(i*ts/tau1)^beta1)
time_gen_V[i]=i*ts
}
F_gen_V<-(convolve(F_gaus_V, F_exp_V,FALSE))+Y0
if(norm==TRUE){
F_gen_V=F_gen_V/max(F_gen_V)}
else{;}
error_V=runif(512,-1*error, error)
for(i in 1:num_points){
F_gen_V[i]=error_V[i]/100*F_gen_V[i]+F_gen_V[i]
sigma[i]=(error_V[i]/100*F_gen_V[i])
}
RETURN=list(time=time_gen_V,y=F_gen_V,sigma=sigma)
if (show_graph==TRUE){
plot(RETURN[[1]],RETURN[[2]], type="l", main="Generated signal with noise",xlab="time, pixel",ylab="Intensity");}
else {;}
return(RETURN)
}

Answer 1

You haven't shown us sim_str_exp, so this example isn't fully reproducible, but I'm going to take a guess here. You say "I generate my own signal with noise", but you use Yexp=sim_str_exp(error=0) to generate the data, so it looks like you're not in fact adding any noise. (Also, your reported RSS at the last step is 1.37e-28 ...)
My guess is that you're running into a problem documented in ?nls, which is that nls() doesn't work well when there is zero noise. This is not documented in ?nlsLM, but I wouldn't be surprised if it held there too.
For convenience, here is the section I'm referring to from ?nls:
Do not use ‘nls’ on artificial "zero-residual" data.
The ‘nls’ function uses a relative-offset convergence criterion
that compares the numerical imprecision at the current parameter
estimates to the residual sum-of-squares. This performs well on
data of the form
y = f(x, theta) + eps
(with ‘var(eps) > 0’). It fails to indicate convergence on data
of the form
y = f(x, theta)
because the criterion amounts to comparing two components of the
round-off error. If you wish to test ‘nls’ on artificial data
please add a noise component, as shown in the example below.
If my hypothesis is correct then you should be able to get a fit without errors if you set the noise amplitude greater than zero.