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....


Xochitl C.


1 Answer 1


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.

Xochitl C.


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