[R] fix sign of a coefficient in formula
Prof Brian Ripley
ripley at stats.ox.ac.uk
Thu Jan 20 11:15:20 CET 2011
Fitting a linear model with constraints is a completely different task
from fitting one without -- and it is the fit you want to constrain,
not the formula.
See CRAN package nnls to fit a linear model with sign constraints. If
you have range constraints you can use nls(algorithm="port") since
'non-linear' here subsumes 'linear'.
In your simple case you can also use some convex optimization theory
to know that if the unconstrained solution has either A < 0 or B < 0
then a solution constrained by A >= 0 and B >= 0 has either A=0 or
B=0 or both, so try those and see which fits best.
On Thu, 20 Jan 2011, Peter Schmidtke wrote:
> Dear R users & experts,
> I'd like to create a model using lm (or glm) under some constraints of
> how coefficients for each component could look like (sort of a range of
> coefficients that should be allowed).
> So let's go for an example :
> model=lm(age ~ eyecolor + height, data=inputdata)
> So let's suppose that R pops out a model with positive estimates for the
> coefficients eyecolor and height, I have to use them as is. But however,
> if I'd like to produce a model that follows that behaviour :
> age = A*eyecolor - B*height
> having A>0 and B>0
Note that in general that will not have an optimal solution. You need
A >= 0 and B >= 0.
Also, that differs from your R formula, which has an intercept and the
opposite sign for 'height'.
> how can I achieve that? I read about offsets, but I just know the range
> of the coefficient, but not the exact value and doing something like
> that offset(seq(-1,0,0.01)*height) doesn't seem to work in lm.
It should work and do what it is documented to do, just not what you
> Thanks in advance for any hint!
> Best regards.
> Peter Schmidtke
> PhD Student
> Dept. Physical Chemistry
> Faculty of Pharmacy
> University of Barcelona
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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