[R] Finding starting values for the parameters using nls() or nls2()

[Andrew Robinson]

Here are some things to try.  Maybe divide Area by 1000 and retention
by 100.  Try plotting the data and superimposing the line that
corresponds to the 'fit' from nls2.  See if you can correct it with
some careful guesses.

Getting suitable starting parameters for non-linear modeling is one of
the black arts of statistical fitting. Good luck!  And don't forget to
check for sensitivity.

Andrew

On 9 October 2016 at 22:21, Pinglei Gao <gaopinglei at 163.com> wrote:
> Hi,
>
> I have some data that i'm trying to fit a double exponential model: data.
> Frame (Area=c (521.5, 689.78, 1284.71, 2018.8, 2560.46, 524.91, 989.05,
> 1646.32, 2239.65, 2972.96, 478.54, 875.52, 1432.5, 2144.74, 2629.2),
>
> Retention=c (95.3, 87.18, 44.94, 26.36, 18.12, 84.68, 37.24, 33.04, 23.46,
> 9.72, 97.92, 71.44, 44.52, 24.44, 15.26) ) and the formula of the double
> exponential is: exp (b0*exp (b1*x^th)).
>
>
>
> I failed to guess the initial parameter values and then I learned a measure
> to find starting values from Nonlinear Regression with R (pp. 25-27):
>
>
>
>> cl<-data.frame(Area =c(521.5, 689.78, 1284.71, 2018.8, 2560.46, 524.91,
> 989.05, 1646.32, 2239.65, 2972.96, 478.54, 875.52, 1432.5, 2144.74, 2629.2),
>
> + Retention =c(95.3, 87.18, 44.94, 26.36, 18.12, 84.68, 37.24, 33.04, 23.46,
> 9.72, 97.92, 71.44, 44.52, 24.44, 15.26) )
>
>> expFct <- function(Area, b0, b1,th) {exp(b0*exp(b1*Area^th))}
>
>> grid.Disperse <- expand.grid(list(b0 = seq(0.01,4, by = 0.01), th =
> c(0.02),b1 = seq(0.01, 4, by = 0.01)))
>
>> Disperse.m2a <- nls2(Retention ~expFct(Area, b0, b1,th), data = cl, start
> = grid.Disperse, algorithm = "brute-force")
>
>> Disperse.m2a
>
> Nonlinear regression model
>
>   model: Retention ~ expFct(Area, b0, th, b1)
>
>    data: cl
>
> b0   th   b1
>
> 3.82 0.02 0.01
>
> residual sum-of-squares: 13596
>
> Number of iterations to convergence: 160000
>
> Achieved convergence tolerance: NA
>
>
>
> I got no error then I use the output as starting values to nls2 ():
>
>> nls.m2<- nls2(Retention ~ expFct(Area, b0, b1, th), data = cl, start =
> list(b0 = 3.82, b1 = 0.02, th = 0.01))
>
> Error in (function (formula, data = parent.frame(), start, control =
> nls.control(),  :
>
> Singular gradient
>
>
>
> Why? Did I do something wrong or misunderstand something?
>
>
>
> Later, I found another measure from Modern Applied Statistics with S (pp.
> 216-217):
>
>
>
>> negexp <- selfStart(model = ~ exp(b0*exp(b1*x^th)),initial =
> negexp.SSival, parameters = c("b0", "b1", "th"),
>
> + template = function(x, b0, b1, th) {})
>
>> Disperse.ss <- nls(Retention ~ negexp(Area, b0, b1, th),data = cl, trace =
> T)
>
>          b0          b1          th
>
>    4.208763  144.205455 1035.324595
>
> Error in qr.default(.swts * attr(rhs, "gradient")) :
>
>  NA/NaN/Inf (arg1) can not be called when the external function is called.
>
>
>
> Error happened again. How can I fix it? I am desperate.
>
>
>
> Best regards,
>
>
>
> Pinglei Gao
>
>
>
>
>         [[alternative HTML version deleted]]
>
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-- 
Andrew Robinson
Deputy Director, CEBRA, School of Biosciences
Reader & Associate Professor in Applied Statistics  Tel: (+61) 0403 138 955
School of Mathematics and Statistics                        Fax: +61-3-8344 4599
University of Melbourne, VIC 3010 Australia
Email: a.robinson at ms.unimelb.edu.au
Website: http://www.ms.unimelb.edu.au/~andrewpr

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