[R] NLS fit for exponential distribution

[peter dalgaard]

On Jun 12, 2011, at 18:57 , Diviya Smith wrote:

> Hello there,
> 
> I am trying to fit an exponential fit using Least squares to some data.
> 
> #data
> x <- c(1 ,10,  20,  30,  40,  50,  60,  70,  80,  90, 100)
> y <- c(0.033823,  0.014779,  0.004698,  0.001584, -0.002017, -0.003436,
> -0.000006, -0.004626, -0.004626, -0.004626, -0.004626)
> 
> sub <- data.frame(x,y)
> 
> #If model is y = a*exp(-x) + b then
> fit <- nls(y ~ a*exp(-x) + b, data = sub, start = list(a = 0, b = 0), trace
> = TRUE)
> 
> This works well. However, if I want to fit the model : y = a*exp(-mx)+c then
> I try -
> fit <- nls(y ~ a*exp(-m*x) + b, data = sub, start = list(a = 0, b = 0, m=
> 0), trace = TRUE)
> 
> It fails and I get the following error -
> Error in nlsModel(formula, mf, start, wts) :
>  singular gradient matrix at initial parameter estimates


If a==0, then a*exp(-m*x) does not depend on m. So don't use a=0 as initial value.

> 
> Any suggestions how I can fix this? Also next I want to try to fit a sum of
> 2 exponentials to this data. So the new model would be  y = a*exp[(-m1+
> m2)*x]+c .

That's not a sum of exponentials. Did you mean a*(exp(-m1*x) + exp(-m2*x)) + c? Anyways, same procedure with more parameters. Just beware the fundamental exchangeability of m1 and m2, so don't initialize them to the same value.

> Any suggestion how I can do this... Any help would be most
> appreciated. Thanks in advance.

-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com