R help - Sep 2011 - NLS error

Hello there,

I am using NLS for fitting a complex model to some data to estimate a couple
of the missing parameters. The model is -
y ~ (C+((log(1-r))*exp(-A*d)*(-1+r+exp(d*(A-B)))/(r*(-A*d+d*B+log(1-r)))))
where A, B and C are unknown.

In order to test the model, I generate data by setting values for all
parameters and add some noise (C).

A <- 20
B <- 500
r <- 0.6881
d <- (1:1000)/1000
y ~
(rnorm(d)*0.005)+(((log(1-r))*exp(-A*d)*(-1+r+exp(d*(A-B)))/(r*(-A*d+d*B+log(1-r)))))

I use Deoptim package to pick the optimum starting values. The model works
fine in most cases, but every now and again, I get the following error -
Error in numericDeriv(form[[3L]], names(ind), env) :
  Missing value or an infinity produced when evaluating the model

Any suggestions on how I can resolve this? Can you suggest a better way for
picking the starting parameters?

Thanks,
Diviya

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Diviya Smith wrote on 09/20/2011 01:03:22 PM:
> 
> Hello there,
> 
> I am using NLS for fitting a complex model to some data to estimate a 
couple
> of the missing parameters. The model is -
> y ~ 
(C+((log(1-r))*exp(-A*d)*(-1+r+exp(d*(A-B)))/(r*(-A*d+d*B+log(1-r)))))
> where A, B and C are unknown.
> 
> In order to test the model, I generate data by setting values for all
> parameters and add some noise (C).
> 
> A <- 20
> B <- 500
> r <- 0.6881
> d <- (1:1000)/1000
> y ~
> (rnorm(d)*0.005)+(((log(1-r))*exp(-A*d)*(-1+r+exp(d*(A-B)))/(r*(-A*d
> +d*B+log(1-r)))))
> 
> I use Deoptim package to pick the optimum starting values. The model 
works
> fine in most cases, but every now and again, I get the following error -
> Error in numericDeriv(form[[3L]], names(ind), env) :
>   Missing value or an infinity produced when evaluating the model
> 
> Any suggestions on how I can resolve this? Can you suggest a better way 
for
> picking the starting parameters?
> 
> Thanks,
> Diviya

I'm not sure if this is the problem, but if r grows greater than 1, 
log(1-r) will be undefined, and you'll get an error.  You can impose a 
constraint on r by rewriting your formula in terms of a variable that can 
take on any real value:
R = log(1-r)

So, 
replace log(1-r) in your formula with R, 
replace (-1 + r) with -exp(R), and 
replace r with 1 - exp(R):
y ~ (C+(R*exp(-A*d)*(-exp(R)+exp(d*(A-B)))/((1 - exp(R))*(-A*d+d*B+R))))

If that doesn't fix the problem, then you are likely getting infinite 
values as result of large numbers in your exponents.  Without example data 
to work through, I can only speculate.

Jean
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