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


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