# Non linear regression - Von Bertalanffy Growth Function - Error: “singular gradient matrix at initial parameter estimates”

I am trying to estimate VBGF parameters K and Linf using non linear regression and nls(). First I used a classic approach where I estimate both parameters together as below with "alkdyr" being a subset per year of my age-length-key database and running in a loop.

vbgf.par <- nls(Lgtcm ~  Linf *(1 - exp(-K * (Age - tzero))), start = c(K= 0.07, Linf = 177.1), data=alkdyr)


I obtain an estimation of both parameters that are strongly correlated. Indeed after plotting Linf ~ K and fitting a linear regression I obtain a function (Linf = a + b*K) with R2= 0.8 and a = 215, b = -763.

In this context, to take into account explicitly correlation between parameters, I decided to fit a new non linear regression derivated from VBGF but where Linf is expressed depending on K (I am most interested in K). To do so, I tried this model:

vbgf.par <- nls(Lgtcm ~  (a + (b*k)) *(1 - exp(-k * (Age - tzero))), start = c(k= 0.07, a= 215, b=-763), data=alkdyr)


Unfortunately at this point I cannot go further as I get the error message "singular gradient matrix at initial parameter estimates".

I tried to use alg= plinear (which I am not sure I understand properly yet). If I give a starting value for a and b only, I have an error message stating "step factor below minFactor" (even when minFactor is set to 100000000000).

Any help will be more than welcome as this is quite urgent....

Best,

Xochitl C.

Packages nlmrt or minpack.lm use a Marquardt method. minpack.lm won't proceed if the Jacobian singularity is at the starting point as far as I'm aware, but nlxb in nlmrt can sometimes get going. It has a policy that is aggressive in trying to improve the sum of squares, so will use more effort than nls when both work.
Answer from J.C. Nash on R mailing list and it works. In my opinion, nlmrt is a particularly good package to realise non linear regression.