# [R] nls start values

Hans W Borchers hwborchers at googlemail.com
Tue Dec 13 16:53:38 CET 2011

```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

```