[R] nls with plinear and function on RHS

[Katharine Mullen]

a) you should put values for Ca, Cb, Cc directly into the data list as
data=list(Ca=1, ....

b) you can simplify the call to

# idealised data set
aDF <- data.frame( x= c(1.80, 9.27, 6.48, 2.61, 9.86, 5.93, 6.76, 5.52,
6.06, 8.62),
y= c(24.77, 2775.07, 895.15, 60.73, 3373.57, 677.82, 1021.92, 542.84,
725.25, 2200.04))

bFunc <- function(x, Cd) cbind(Ca=1,Cb=x, Cc=x^Cd)

# nls, plinear algorithm, RHS from function
nls(y ~ bFunc(x, Cd), data=list(x=aDF$x, y=aDF$y),
    start=list(Cd=3), algorithm="plinear")

On Thu, 2 Oct 2008, Keith Jewell wrote:

> Dear R gurus,
>
> As part of finding initial values for a much more complicated fit I want to
> fit a function of the form y ~ a + bx + cx^d to fairly "noisy" data and have
> hit some problems.
>
> To demonstrate the specific R-related problem, here is an idealised data
> set, smaller and better fitting than reality:
> # idealised data set
> aDF <- data.frame( x= c(1.80, 9.27, 6.48, 2.61, 9.86, 5.93, 6.76, 5.52,
> 6.06, 8.62),
> y= c(24.77, 2775.07, 895.15, 60.73, 3373.57, 677.82, 1021.92, 542.84,
> 725.25, 2200.04))
>
> And here are some starting values, far better than I'd have in reality
> # good starting values
> startL <- list(Ca=4, Cb=3, Cc=3, Cd=3)
>
> In these idealised circumstances nls converges using the default algorithm.
> # nls, default algorithm
> nls(y ~ Ca + Cb*x + Cc*x^Cd, data=aDF, start=startL)
>
> Unfortunately, in reality it often fails to converge. This model is linear
> in a, b and c so I've used the plinear algorithm.
> # nls, plinear algorithm, explicit RHS
> nls(y ~ cbind(Ca=1,Cb=x, Cc=x^Cd), data=aDF, start=startL["Cd"],
> algorithm="plinear")
>
> This converges much more often but sometimes crashes with the error message
> "Error in numericDeriv(form[[3]], names(ind), env) :
>   Missing value or an infinity produced when evaluating the model"
>
> I deduce that it is failing in the numerical differentiation of x^Cd (but
> don't know why), so I thought I'd avoid the numerical differentiation by
> putting the RHS in a function to which I could (later) add a 'gradient'
> attribute
> # function to provide RHS
> bFunc <- function(x, Ca, Cb, Cc, Cd) cbind(Ca=1,Cb=x, Cc=x^Cd)
>
> # nls, plinear algorithm, RHS from function
> nls(y ~ bFunc(x, Ca, Cb, Cc, Cd), data=aDF, start=startL["Cd"],
> algorithm="plinear")
>
> However, this gives me
> "Error in nls(y ~ bFunc(x, Ca, Cb, Cc, Cd), data = aDF, start =
> startL["Cd"],  :
>   parameters without starting value in 'data': Ca, Cb, Cc"
>
> Can anyone tell me
> a) why putting the RHS into a function "broke" the plinear algorithm
> b) if there's a better approach to my problem
>
> Thanks in advance,
>
> Keith Jewell
> -----------------
> I'm using V2.7.2...
> > sessionInfo()
> R version 2.7.2 (2008-08-25)
> i386-pc-mingw32
>
> locale:
> LC_COLLATE=English_United Kingdom.1252;LC_CTYPE=English_United
> Kingdom.1252;LC_MONETARY=English_United
> Kingdom.1252;LC_NUMERIC=C;LC_TIME=English_United Kingdom.1252
>
> attached base packages:
> [1] stats     graphics  grDevices datasets  tcltk     utils     methods
> base
>
> other attached packages:
> [1] xlsReadWrite_1.3.2 svSocket_0.9-5     TinnR_1.0.2        R2HTML_1.59
> Hmisc_3.4-3
>
> loaded via a namespace (and not attached):
> [1] cluster_1.11.11 grid_2.7.2      lattice_0.17-14 svMisc_0.9-5
> VGAM_0.7-7
>
> ... but have also tried todays V2.7.2 patched and V2.8.0alpha, both of which
> give the same behaviour
>
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