Hello colleagues,
I am attempting to determine the nonlinear least-squares estimates of
the nonlinear model parameters using nls. I have come across a common
problem that R users have reported when I attempt to fit a particular
3-parameter nonlinear function to my dataset:
Error in nls(r ~ tlm(a, N.fix, k, theta), data = tlm.data, start list(a = a.st,
:
step factor 0.000488281 reduced below `minFactor' of 0.000976563
Despite modifying minFactor using nls.control, I am unable to counter
the apparent singularity in the model fit. I have also tried changing
the tolerance and start parameter values to no avail. If anyone can
provide a relatively simple solution (perhaps adjusting the gradient,
but I'm not sure how to do this), I would be most appreciative. My
dataset is:
> tlm.data
r N.fix
1 -0.52407085 76
2 0.10536052 45
3 -0.17435339 50
4 0.19415601 42
5 0.48701498 51
6 -0.50681760 83
7 -0.17435339 50
8 0.55278982 42
9 0.15219182 73
10 0.49899117 85
11 0.10821358 140
12 -0.83034830 156
13 -0.30748470 68
14 -0.22314355 50
15 0.04879016 40
16 -0.04879016 42
17 0.75377180 40
18 -0.12516314 85
19 -0.36624439 75
My function is:
tlm <- function(a,N,k,theta) (a*(1-((N/k)^theta)))
The nls fit I've coded is:
tlm.fit <- try(nls(r~tlm(a,N.fix,k,theta), data=tlm.data,
start=list(a=a.st,k=k.st,theta=1),
trace=TRUE,
control=nls.control(maxiter=6000,tol=1e-05,minFactor=1/1024)))
I'm using start values parsed in from another (previous, but not shown)
model fit. In this case,
> a.st
[1] 0.3812922
> k.st
[1] 64.66529
I happen to know the true values for the optimised parameters (from
another application), but I can't get nls to reproduce them. They are:
a = 2.0466
k = 60.8275
theta = 0.2277
Any ideas?
Regards,
Corey Bradshaw
[[alternative HTML version deleted]]
Corey Bradshaw <corey.bradshaw <at> cdu.edu.au> writes: : I am attempting to determine the nonlinear least-squares estimates of : the nonlinear model parameters using nls. I have come across a common : problem that R users have reported when I attempt to fit a particular : 3-parameter nonlinear function to my dataset: : : Error in nls(r ~ tlm(a, N.fix, k, theta), data = tlm.data, start : list(a = a.st, : Try it with nlm. I find I often have better luck that with it.
"Corey Bradshaw" <corey.bradshaw at cdu.edu.au> writes:> Hello colleagues, > > > > I am attempting to determine the nonlinear least-squares estimates of > the nonlinear model parameters using nls. I have come across a common > problem that R users have reported when I attempt to fit a particular > 3-parameter nonlinear function to my dataset: > > > > Error in nls(r ~ tlm(a, N.fix, k, theta), data = tlm.data, start > list(a = a.st, : > > step factor 0.000488281 reduced below `minFactor' of 0.000976563 > >....> My function is: > > > > tlm <- function(a,N,k,theta) (a*(1-((N/k)^theta))) > > > > The nls fit I've coded is: > > > > tlm.fit <- try(nls(r~tlm(a,N.fix,k,theta), data=tlm.data, > start=list(a=a.st,k=k.st,theta=1), > > trace=TRUE, > control=nls.control(maxiter=6000,tol=1e-05,minFactor=1/1024)))When you wrap the expresssion to fit in the tlm function, you are effectively keeping nls from using algebraic derivatives and forcing it to do something like dtlm/da =~ (tlm(a+1e-7,...) - tlm(a,...))/1e-7. So you might try sticking in the actual expression r ~ a * (1 - (N.fix/k)^theta) or modify tlm to return a gradient attribute. Reparametrizing in terms of log(k) might also help keeping you out fo trouble. -- O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
Corey Bradshaw wrote:> Hello colleagues, > > > > I am attempting to determine the nonlinear least-squares estimates of > the nonlinear model parameters using nls. I have come across a common > problem that R users have reported when I attempt to fit a particular > 3-parameter nonlinear function to my dataset: > > > > Error in nls(r ~ tlm(a, N.fix, k, theta), data = tlm.data, start > list(a = a.st, : > > step factor 0.000488281 reduced below `minFactor' of 0.000976563 > > > > Despite modifying minFactor using nls.control, I am unable to counter > the apparent singularity in the model fit. I have also tried changing > the tolerance and start parameter values to no avail. If anyone can > provide a relatively simple solution (perhaps adjusting the gradient, > but I'm not sure how to do this), I would be most appreciative. My > dataset is: > > > > >>tlm.data > > > r N.fix > > 1 -0.52407085 76 > > 2 0.10536052 45 > > 3 -0.17435339 50 > > 4 0.19415601 42 > > 5 0.48701498 51 > > 6 -0.50681760 83 > > 7 -0.17435339 50 > > 8 0.55278982 42 > > 9 0.15219182 73 > > 10 0.49899117 85 > > 11 0.10821358 140 > > 12 -0.83034830 156 > > 13 -0.30748470 68 > > 14 -0.22314355 50 > > 15 0.04879016 40 > > 16 -0.04879016 42 > > 17 0.75377180 40 > > 18 -0.12516314 85 > > 19 -0.36624439 75 > > > > My function is: > > > > tlm <- function(a,N,k,theta) (a*(1-((N/k)^theta))) > > > > The nls fit I've coded is: > > > > tlm.fit <- try(nls(r~tlm(a,N.fix,k,theta), data=tlm.data, > start=list(a=a.st,k=k.st,theta=1), > > trace=TRUE, > control=nls.control(maxiter=6000,tol=1e-05,minFactor=1/1024))) > > > > I'm using start values parsed in from another (previous, but not shown) > model fit. In this case, > > > > >>a.st > > > [1] 0.3812922 > > >>k.st > > > [1] 64.66529 > > > > I happen to know the true values for the optimised parameters (from > another application), but I can't get nls to reproduce them. They are: > > > > a = 2.0466 > > k = 60.8275 > > theta = 0.2277 > > > > Any ideas? > > > > Regards, > > Corey Bradshaw >It is possible to fit this model to these data using nls as shown in the enclosed transcript. You have one conditionally linear parameter ('a') in the model so I used the plinear algorithm and I also generated analytic derivatives for the tls function using the deriv function. There are several things to note: - Your data are very noisy. It is not surprising that it is difficult to fit a 3-parameter nonlinear model to such data. - The fitted model has negative values for both 'a' and 'theta'. - The estimates are highly imprecise. > summary(fm1) Formula: r ~ tlm(N.fix, k, theta) Parameters: Estimate Std. Error t value Pr(>|t|) k 49.0724 6.9153 7.096 2.53e-06 theta -4.6676 5.1805 -0.901 0.381 .lin -0.2333 0.1685 -1.385 0.185 Residual standard error: 0.3662 on 16 degrees of freedom Correlation of Parameter Estimates: k theta theta 0.8353 .lin -0.3458 -0.7104 -------------- next part -------------- An embedded and charset-unspecified text was scrubbed... Name: nls.Rout Url: https://stat.ethz.ch/pipermail/r-help/attachments/20050223/a9055f2d/nls.pl