[R] nls vs nlme: parameter constraints

[Dieter Menne]

Manuel Morales wrote:
> 
> I'm trying to fit a model like beta[trt]/(1+alpha*x) where the data
> include some grouping factor. The problem is that the estimate for alpha
> is undefined for some of the treatments - any value greater than 20 is
> equally good and a step function would suffice. Ignoring the grouping
> structure, I can fit this using nls with the port algorithm by
> restricting the upper value of alpha to 20. Is there a way to do
> something similar in nlme?
> 


Manuel Morales <Manuel.A.Morales <at> williams.edu> writes:

> I'm trying to fit a model like beta[trt]/(1+alpha*x) where the data
> include some grouping factor. The problem is that the estimate for alpha
> is undefined for some of the treatments - any value greater than 20 is
> equally good and a step function would suffice. Ignoring the grouping
> structure, I can fit this using nls with the port algorithm by
> restricting the upper value of alpha to 20. Is there a way to do
> something similar in nlme?

A step functions would not help, but nlme will converge if  alpha is not
included in the random  = ... term, so effectively making it fixed. It is
the great power of nlme that it works even when only half of the nls fits
converge because of  the cooperative effect of the population fit.

I have seen many examples where using a population-fixed parameter works
like restrictions on steroids. In population pharmakokinetics, this approach
is fairly standard, but rather unknown to the rest of the world.

See the discussion on page 370 of Pinheiro/Bates (chapter 8.2). 

Dieter


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