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fix sign of a coefficient in formula

2 messages · Peter Schmidtke, Brian Ripley

Peter Schmidtke
# 
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

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.

Thanks in advance for any hint!

Best regards.
Brian Ripley
# 
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:

            

      
      
      
    

        
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'.

            

      
      
      
    

        
It should work and do what it is documented to do, just not what you 
want.