[R] nls start values

[Bert Gunter]

Niklaus:

1. First, you mat not need to use nls at all, although I am not
familiar with the "port" algorithm, so I could very well be wrong
about this.  Generally speaking, one uses time series methods (e.g.
fourier analysis) to fit periodic sine waves, so you may wish to check
out CRAN's TimeSeries task view to see whether there is something
there that fits your constrained fit situation.

2. If you DO need to fit a nonlinear function the  short answer to
your questions is maybe/maybe not; obviously, Hans's suggestions may
help you get a better starting point but it still usea the same
sensitive algorithm, which is some version of gradient descent iirc.
The optimx package contains a varied collection of optimizers, some of
which may well be more robust than that of nls2. Check out that
package and the Optimization task view for background, references, and
alternatives (such as derivative-free optimizers)

Cheers,

Bert

On Tue, Dec 13, 2011 at 7:53 AM, Hans W Borchers
<hwborchers at googlemail.com> wrote:
> Niklaus Fankhauser <niklaus.fankhauser <at> cell.biol.ethz.ch> writes:
>
>> I'm using nls to fit periodic gene-expression data to sine waves. I need
>> to set the upper and lower boundaries, because I do not want any
>> negative phase and amplitude solutions. This means that I have to use
>> the "port" algorithm. The problem is, that depending on what start value
>> I choose for phase, the fit works for some cases, but not for others.
>> In the example below, the fit works using phase=pi,  but not using
>> phase=0. But there are many examples which fit just fine using 0.
>>
>> Is there a comparable alternative to nls that is not so extremely
>> influenced by the start values?
>>
>
> Use package `nls2' to first search on a grid, and then apply `nls' again
> to identify the globally best point:
>
>    # Data for example fit
>    afreq <- 1 / (24 / 2 / pi)
>    tpoints <- c(0,0,0,2,2,2,4,4,4,6,6,6,8,8,8,12,12,12,
>                 14,14,14,16,16,16,18,18,18,20,20,20,24,24,24)
>    gene_expression <-
>    c(1.551383, 1.671742, 1.549499, 1.694480, 1.632436, 1.471568, 1.623381,
>      1.579361, 1.809394, 1.753223, 1.685918, 1.754968, 1.963069, 1.820690,
>      1.985159, 2.205064, 2.160308, 2.120189, 2.194758, 2.165993, 2.189981,
>      2.098671, 2.122207, 2.012621, 1.963610, 1.884184, 1.955160, 1.801175,
>      1.829686, 1.773260, 1.588768, 1.563774, 1.559192)
>    shift=mean(gene_expression) # y-axis (expression) shift
>
>    # Grid search
>    library("nls2")
>    frml <- gene_expression ~ sin(tpoints * afreq + phase) * amp + shift
>    startdf <- data.frame(phase=c(0, 2*pi), amp = c(0, 2))
>    nls2(frml, algorithm = "grid-search", start = startdf,
>               control = list(maxiter=200))
>
>    # Perfect fit
>    startvals <- list(phase = 4.4880, amp = 0.2857)
>    sine_nls <- nls(frml, start=startvals)
>    #  phase    amp
>    # 4.3964 0.2931
>    # residual sum-of-squares: 0.1378
>
> Maybe this can be done in one step.
> Hans Werner
>
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-- 

Bert Gunter
Genentech Nonclinical Biostatistics

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