[R] non-linear regression and root finding

[Ivan Krylov]

On Mon, 6 Nov 2023 14:55:39 -0500
J C Nash <profjcnash using gmail.com> wrote:

> However, I'm wondering if this approach is worth writing up, at least
> as a vignette or blog post. It does need a shorter example and some
> explanation of the "why" and some testing perhaps.

Do you mean using this problem as a basis to illustrate ordering
constraints on parameters? Weird constraints do come up every now and
then in regression problems. I could definitely offer my help with at
least some of the text.

> If there's interest, I'll be happy to join in. And my own posting
> suggests how the ordering is enforced by bounding the "delta"
> parameters from below.

I have just tried nlsr::nlxb for a slightly larger dataset shared by
Troels off-list, and it worked great with the delta parameters as you
suggested, thank you!

It's interesting that nlxb and nlsLM give slightly different answers,
differing in 0.5 pK units for pK1 and (pK2-pK1) but not (pK3-pK2). Then
again, they both agree that the standard error for pK1 and (pK2-pK1) is
very large, so perhaps the problem is just very ill-conditioned.

-- 
Best regards,
Ivan