Hi All,
I've found a few references in the mailing list and documentation to
constrained least squares fitting, but little on restrained least squares.
To clarify what I mean, a constraint might limit a parameter to a particular
value (e.g. x=5.0, or exactly within the bounds 4.9 - 5.1), whereas a
restraint adds some further information to the problem about the certainty
of the starting point for the parameter (e.g. x=5.0, +/- 0.1, but it is able
to vary outside of this range if the data strongly supports it). By
extension, the output of a function can be restrained to a value, for
example x+log(y)=1.0+/-0.2. This is common in the world of crystallography,
where e.g. an atom to atom bond-length can be restrained to a sensible value
in order to prevent "explosion" of a difficult non-linear least
squares
problem.
The "do it yourself" approach is to minimise the (weighted) sum of
squared
residuals PLUS the (weighted) sum of squared residuals from the restraint
estimates - however given the plethora of good fitting functions in R, I
thought this might be available as standard in some package or other.
If I am merely a victim of terminology, in that what crystallographers call
restrained least squares is called something different by statisticians and
this is included in a standard package, please just point me at the
appropriate FAQ or function. I have a suspicion that "penalised least
squares" might be related, but haven't seen any examples that jump out
at me
as exactly what I'm after.
Cheers
Shamus
--
Dr. Shamus Husheer
Cambridge Temperature Concepts
www.temperatureconcepts.com
Cambridge Temperature Concepts Limited is a UK registered company (company
number 5943341, VAT number 922051171), with registered offices at Downing
Enterprise, Downing College, University of Cambridge, Regent Street,
Cambridge CB2 1DQ, United Kingdom. The contents of this email and
attachments are confidential. If you are not the intended recipient, please
inform me by reply email and delete this message and any attachments.
[[alternative HTML version deleted]]
