# [R] nls problem

William Dunlap wdun|@p @end|ng |rom t|bco@com
Thu Apr 2 18:50:05 CEST 2020

```Roundoff/cancelation error: compare the following.  The first is equivalent
to your function, the last to fitted().

> with(aedf, t(cbind(1, pH, pH^2) %*% round(coef(m), digits=2)))
[,1]      [,2]       [,3]         [,4]       [,5]       [,6]
[,7]       [,8]       [,9]     [,10]
[1,] -0.01635965 0.1076024 0.07477337 -0.007166685 -0.1337865 -0.2851877
-0.4804638 -0.6865135 -0.9870137 -1.398027
> with(aedf, t(cbind(1, pH, pH^2) %*% round(coef(m), digits=4)))
[,1]        [,2]       [,3]       [,4]       [,5]       [,6]
[,7]      [,8]      [,9]     [,10]
[1,] -0.2196286 -0.09864071 -0.1345213 -0.2180792 -0.3463237 -0.4991861
-0.6959856 -0.903394 -1.205598 -1.618608
> with(aedf, t(cbind(1, pH, pH^2) %*% round(coef(m), digits=16)))
[,1]        [,2]       [,3]       [,4]       [,5]      [,6]
[,7]       [,8]      [,9]     [,10]
[1,] -0.2208705 -0.09989926 -0.1357969 -0.2193638 -0.3476174 -0.500488
-0.697296 -0.9047119 -1.206926 -1.619947

Note that your model is linear and could be fitted with
lm(data=aedf, Flux ~ pH + I(pH^2))
lm(data=aedf, Flux ~ poly(pH, 2))
The latter uses a more stable parameterization.

Bill Dunlap
TIBCO Software
wdunlap tibco.com

On Thu, Apr 2, 2020 at 4:15 AM Troels Ring <tring using gvdnet.dk> wrote:

> Dear friends - I'm on Win10 with R 6.3.1 and have a very simple problem
> with
> nls which apparently gives a decent fit to the parable below, even without
> starting values. But when I then think I know the meaning of the three
> parameters a, b, and d it goes very wrong. I guess I am again overlooking
> something easy but cannot spot it.
>
> BW
> Troels Ring,
>
> Aalborg, Denmark
>
>
>
>
>
> aedf <- structure(list(Flux = c(-0.141256, -0.154709, -0.215247,
> -0.302691,
>
>             -0.32287, -0.511211, -0.605381, -0.813901, -1.11659, -1.76906
>
> ), pH = c(7.06273, 7.11182, 7.16182, 7.18818, 7.21455, 7.23818,
>
>           7.26273, 7.28455, 7.31182, 7.34364)), class = "data.frame",
> row.names = c(NA,
>
>
> -10L))
>
> m <- with(aedf,nls(Flux~a + b*pH + d*pH^2))
>
>
>
> with(aedf,plot(pH,Flux))
>
> with(aedf,lines(pH,fitted(m),lty=1,col="red",lwd=3))
>
>
>
> m
>
> # a        b        d
>
> # -1630.70   457.67   -32.11
>
>
>
> fitted(m)
>
> # 1] -0.22087053 -0.09989926 -0.13579690 -0.21936385 -0.34761742
> -0.50048799
>
> # [7] -0.69729602 -0.90471194 -1.20692552 -1.61994657
>
>
>
> FPG <- function(pH) -1630.70 + 457.67*pH -32.11*pH^2
>
>
>
> FPG(aedf\$pH)
>
> # [1] -0.016359649  0.107602395  0.074773375 -0.007166685 -0.133786467
>
> # [6] -0.285187665 -0.480463769 -0.686513537 -0.987013685 -1.398026917
>
>
>
> # So why aren't fitted(m) and FPG(aedf\$pH) not closer ("equal")?
>
>
>
>
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>
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>
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