[R] Really stuck with the nls function!! It's Urgent !!

[oussama belmejdoub]

Greetings,

I'm trying to use the nls function in my statistics project but I'm really finding lot of difficulties.

I have a function called apinene_modele_prediction that calculates the estimations:
library(expm); #exp of a matrixapinene_modele_prediction <- function(t,theta) {x0=c(100,0,0,0,0);A=matrix(c(-(theta[1]+theta[2]),theta[1],theta[2],0,0,0,0,0,0,0,0,0,-(theta[3]+theta[4]),theta[3],theta[4],0,0,0,0,0,0,0,theta[5],0,-theta[5]),5,5);X=x0;for (i in t[2:length(t)]){X=c(X,x0%*%expm(A*i));}return(X);}
 
My "t" vector is given by: 
t=seq(0,100,by=2)
And the real observations "y" ara given to us  in a txt file called "data.txt" that I have joined to this message.

So when I try to fit the "theta" in my model starting with: theta=c(0.2,0.2,0.2,0.2,0.2) 
And doing:
theta_appr <-nls(y~apinene_modele_prediction(t,theta),start=list(theta=c(0.2,0.2,0.2,0.2,0.2)))
I always get the ERROR : singular gradient matrix at initial parameter estimates

And, when I try: nls(y~apinene_modele_prediction(t,c(theta,theta,theta,theta,theta)),start=list(theta=0.2))
I get the result:Nonlinear regression model  model: y ~ apinene_modele_prediction(t, c(theta,theta,theta,theta,theta))data: parent.frame()theta 0.04403residual sum-of-squares: 219002


But I need to have the elements of the theta to be different and not equal.
Thanks in advance for your help. 		 	   		  
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