> On 10 Oct 2016, at 00:40 , Bert Gunter <bgunter.4...@gmail.com> wrote:
>
> Well... (inline -- and I hope this isn't homework!)
>
Pretty much same as I thought.
Fixing th=0.02 in the grid search looks wrong. Bert's plot is pretty linear, so
th=1 is a good guesstimate. There's a slight curvature but to reduce it, you
would increase th, not decrease it. Running the regression, as Bert suggests,
indicates that b0=5.16 and b1= -0.00024 could work as reasonable starting
values. Notice that the grid search had "b1 = seq(0.01, 4, by = 0.01)" which is
wrong in both sign and scale.
Andrew's suggestion of dividing Retention by 100 is tempting, since it looks
like a percentage, but that would make all Y values less than 1 and the double
exponential function as written has values that are always bigger than 1. (It
is conceivable that the model itself is wrong, though. E.g. it could be that
Retention on a scale from 0 to 1 could be modeled as exp(-something), but we
really have no idea of the context here.)
(If this was in fact homework, you should now go and write a proper SelfStart
initializer routine for this model. Even if it isn't homework, you do need to
study the text again, because you have clearly not understood how self-starting
models work.)
-pd
>
>
>
> On Sun, Oct 9, 2016 at 3:05 PM, Andrew Robinson
> <a.robin...@ms.unimelb.edu.au> wrote:
>> 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. ...
>>
>> Andrew
>
> True. But it's usually worthwhile thinking about the math a bit before
> guessing.
>
> Note that the model can be linearized to:
>
> log(log(Retention)) = b0 + b1*Area^th
>
> So a plot of log(log(Retention)) vs Area may be informative and useful
> for finding starting values. e.g., for a grid of th's, do linear
> regression fits .
>
> However, when I look at that plot, it seems pretty linear with a
> negative slope. This suggests that you may have an overparametrization
> problem . i.e. fix th =1 and use the b0 and b1 from the above
> regression for starting values.
>
> Do note that this strategy isn't foolproof, as it ignores that the
> error term is additive in the above transformed metric, rather than
> the original. This can sometimes mislead. But this is just a
> heuristic.
>
> Cheers,
> Bert
>
>
>
>
>
>
>
>>
>> On 9 October 2016 at 22:21, Pinglei Gao <gaoping...@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]]
>>>
>>> ______________________________________________
>>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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>>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>>
>> --
>> 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.robin...@ms.unimelb.edu.au
>> Website: http://www.ms.unimelb.edu.au/~andrewpr
>>
>> MSME: http://www.crcpress.com/product/isbn/9781439858028
>> FAwR: http://www.ms.unimelb.edu.au/~andrewpr/FAwR/
>> SPuR: http://www.ms.unimelb.edu.au/spuRs/
>>
>> ______________________________________________
>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd....@cbs.dk Priv: pda...@gmail.com
______________________________________________
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