[R] Non linear regression - Von Bertalanffy Growth Function - "singular gradient matrix at initial parameter estimates"

[Xochitl CORMON]

Dear all,

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 derivate 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.




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Xochitl CORMON
+33 (0)3 21 99 56 84

Doctorante en écologie marine et science halieutique
PhD student in marine ecology and fishery science

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