[R] Covariates in NLS (Multiple nonlinear regression)

[Lindsay Banin]

Dear R-users,

I am trying to create a model using the NLS function, such that:

Y = f(X) + q + e

Where f is a nonlinear (Weibull: a*(1-exp(-b*X^c)) function of X and q is a covariate (continous variable) and e is an error term. I know that you can create multiple nonlinear regressions where x is polynomial for example, but is it possible to do this kind of thing when x is a function with unknown coefficients (a,b,c)? Ultimately, I am expecting the output to give individual regression models for each coefficient (a,b,c) with q as a covariate.

I have tried the following code, and get the resultant error messages:
> weib.nls <- nls(Y ~ (a*(1-exp(-b*X^c)))|q,
> + data=DATA,
> + start=c(a=75,b=0.05,c=0.7))
> Error in nlsModel(formula, mf, start, wts) : 
>   singular gradient matrix at initial parameter estimates
> > summary(weib.nls)

> > weib.nls2 <- nls(Y~ (a*(1-exp(-b*X^c)))+q,
> + data=DATA,
> + start=c(a=75,b=0.05,c=0.7))
> Error in numericDeriv(form[[3L]], names(ind), env) : 
>   Missing value or an infinity produced when evaluating the model
> 

Many thanks in advance!
Lindsay